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The main objective of this paper is to provide a reliable experimental methodology that utilizes biaxial tension and shear loading combined with appropriate butterfly specimens for characterizing forming limits at fracture (FLF) for aluminum alloy 6K21-T4 sheets over a wide range of strain paths. To realize the goal, the performance of an existing butterfly specimen for fracture testing of the aluminum sheet is first experimentally and numerically studied. Experimental and numerical results show that premature edge fracture may easily occur on the aluminum sheet specimen under combined tension and shear loading, which would lead to a high degree of uncertainty for the measured limit strains at fracture. To solve the problem and provide a reliable testing method, optimized butterfly specimens are proposed, and their performance for fracture testing of the aluminum sheet is numerically evaluated. Subsequently, verification experiments on the optimized butterfly specimens extracted from the aluminum sheet are conducted under seven different combined tension and shear loading conditions and a strain-rate-based time-dependent method combined with the image inspection of specimen surface is presented to determine the onset of fracture. Experimental results show that the forming limit strains at fracture in arbitrary strain paths between simple shear and plane strain can be accurately obtained by using the proposed experimental methodology. In addition, three newly proposed ductile fracture criteria (Lou−Huh 2012, MMC3, and Hu−Chen) are employed to predict the FLF for the aluminum 6K21-T4 sheet over a wide range of strain paths. It is found that the Hu−Chen model exhibits the best prediction capability for the FLF.

Common practice for the integrity assessment of structures, follows the use of Fitness for Service procedures, such as BS 7910/R6. There are many common structures (e.g. pipes) that are under biaxial loading. Even though the load biaxiality has been proven experimentally to have an effect on both the fracture toughness and the limit load of a component, the influence of biaxial stresses is not always directly addressed in the procedures. In order to address the effect of biaxiality on engineering critical assessments, BS 7910 and R6 fitness for service procedures are applied to four biaxially loaded wide plate tests previously conducted on A533B steel. The plates had been loaded in biaxial tension, with different biaxiality ratios, while the temperatures of the plates tested correspond to lower transition fracture toughness. The assessments include failure assessment lines created using Option 1, which requires the knowledge of the yield stress and tensile strength, Option 3 which is a material, structure and load dependent option, as well as a constraint modified Option 3 failure assessment line. To obtain Option 3 failure assessment lines, finite element analyses are conducted for the specimens. The tests are first assessed with the proximity to plastic collapse (Lr) and fracture (Kr) being calculated with the use of the main fracture clauses of BS 7910/R6, which do not take into account the effects of biaxiality. The conventional assessment is then followed by a more detailed assessment using the values calculated from Finite Element Analyses (FEA).

In tissue engineering (TE) strategies, cell processes are regulated by mechanical stimuli. Although TE scaffolds have been developed to replicate tissue-level mechanical properties, it is experimentally prohibitive to measure and prescribe the cellular micromechanical environment (CME) generated within these constructs. Accordingly, this study aimed to fill this lack of understanding by modelling the CME in TE scaffolds using the finite element method. A repeating unit of composite fiber scaffold for annulus fibrosus repair with a fibrin hydrogel matrix was prescribed a series of loading, material, and architectural parameters. The CME was predicted and the corresponding cell phenotypes were predicted based on previously hypothesized criteria. Scaffold multi-axial loading was demonstrated as the most pertinent parameter contributing to the CME criteria being satisfied. Specifically, radial-direction compression with biaxial tension lead to a prediction of regeneration for 66.5% of the cell volumes. Additionally, the architectural scale had a moderate influence on the CME with minimal change in the tissue-level properties of the scaffold. All other scaffold materials and architectures considered had secondary influences on the predicted regeneration by modifying the scaffold loading. By predicting the regeneration potential of different scaffold designs, the developed high-fidelity computational tool described in this study enables for a more comprehensive understanding of the relationship between tissue-level and cell-level mechanics for a broad range of tissue engineering applications.

The relationship between void size/location and mechanical behavior under biaxial loading of copper nanosheets containing voids are investigated by molecular dynamics method. The void location and the void radius on the model are discussed in the paper. The main reason of break is discovered by the congruent relationship between the shear stress and its dislocations. Dislocations are nucleated at the corner of system and approached to the center of void with increased deformation. Here, a higher stress is required to fail the voided sheets when smaller voids are utilized. The void radius influences the time of destruction. The larger the void radius is, the lower the shear stress and the earlier the model breaks. The void location impacts the dislocation distribution.

This paper investigates the failure behavior of three-dimensional (3D) braided composites subjected to biaxial tension and compression through an improved micromechanical computational method and the finite element (FE) method. The yarns and the out-of-yarn matrix in the composites are modeled by an extended Hashin criterion and an extended Drucker-Prager criterion, respectively. The uniaxial mechanical properties are analyzed based on the available experimental data as a verification of the models. The biaxial progressive damage and failure behavior are investigated using the models. The braiding structure, whose diversity results in the difference in failure modes during damage evolution, has significant influence on the biaxial failure correlation of the composites. The predicting formulae for failure envelopes are suggested in this study. The failure envelopes of 3D four-directional and five-directional braided composites can be described by quadratic tensor theories, and the envelopes of 3D six-directional and seven-directional braided composites can be predicted by the maximum strain criterion.

In this study, creep damage in a biaxially creep-damaged Mod.9Cr–1Mo component has been examined via uniaxial miniature creep testing. Using cruciform specimens, biaxial tension creep tests were conducted at principal stress ratios (λ) of λ = 0.0 and 1.0 at 923 K. The principal stress ratio is the ratio of the y-directional principal stress ( σ y ) to the x-directional principal stress ( σ x ) in a cruciform specimen ( λ = σ y / σ x ). The equi-biaxial creep test was interrupted at a half lifetime, and two miniature specimens were machined from the damaged cruciform specimen in the x- and y-direction. The applicability of the linear cumulative creep damage rule was assessed using the results of the miniature lifetimes. The linear cumulative creep damage rule gave an unconservative estimate to the remaining life of a biaxially damaged cruciform specimen. Using the hyperbolic constitutive relationship, the unconservative estimate according to the damage accumulation was explained.

Under creep regime, the multiple cracks would remarkably deteriorate the service life of the component with respect to the case of a single crack due to the higher C* values induced by the interaction and coalescence of the adjacent cracks. In this paper, the creep interaction effect of two identical coplanar surface flaws in a plate subjected to biaxial tension loads were calculated under various crack configurations, creep properties and biaxial stress ratios. The results revealed that the creep interaction level was greatly dependent on crack depth, crack distance, creep exponent and biaxial stress ratio whereas crack shape had little influence. In addition, the creep interaction factor determined by the average C* values along the crack front could better represent the multiple cracks interaction under biaxial stress state. Finally, an empirical equation for the creep interaction factor was established on the basis of the comprehensive finite element analyses and the size of the equivalent single crack replacing the interacted multiple cracks should be determined by the creep interaction factor.

A comparative study on the dynamic properties of dam and sieved concrete was conducted based on dynamic biaxial tensile-compressive tests. Specimens were designed to be prismatic shape with a size of 250 × 250 × 400 mm for dam concrete and 150 × 150 × 300 mm for sieved concrete, respectively. Each specimen was biaxially loaded by constant tensile-compressive (T-C) stress ratios (0:−1, 0.05:−1, 0.1:−1, 0.25:−1, 0.5:−1, and ∞) at the strain rate of 10 −5 s −1 , 10 −4 s −1 , 10 −3 s −1 , and 10 −2 s −1 by a servo-hydraulic multi-axial testing machine. The failure modes of specimens have been compared under various biaxial T-C loading conditions at each strain rate, thus the fracture surface of sieved concrete specimen is smoother than dam concrete. The dynamic strength of dam concrete is lower than sieved concrete under the same loading condition, and the ratio of them is insensitive to strain rate. The growth rates of dynamic strength for dam concrete is consistent with sieved concrete, whereas much larger than ordinary concrete. By regression of the test results, the dynamic T-C failure criterions for dam and sieved concrete were proposed after considering the combined effects of strain rate and stress ratio.

Experimental data are needed to evaluate constitutive models. The richer the experimental data, in terms of different deformation modes for example, the better the constraints on the model. To this end, the mechanical response of glassy polycarbonate (PC) is studied using biaxial tension experiments with novel sample geometries. Deformation fields are measured using full-field digital image correlation (DIC) to reveal a large difference in the strain localisation behaviour of the material depending on the amount of lateral deformation. The difference in the localisation behaviour is also reflected in the macroscopic force-displacement response. The experimental data acquired in the experiments are used to examine the ability of a physically-motivated constitutive model to predict the mechanical response of the material during biaxial deformation. To improve the numerical predictions, the elastic part of the constitutive model is modified such that the initial non-linear response due to volumetric deformation is accurately captured. This new elastic model is motivated by the experimental results, which show that the commonly used quadratic form of the elastic free energy results in a too stiff response during biaxial tension.

The tricuspid valve ensures unidirectional blood flow from the right atrium to the right ventricle. The three tricuspid leaflets operate within a dynamic stress environment of shear, bending, tensile, and compressive forces, which is cyclically repeated nearly two billion times in a lifetime. Ostensibly, the microstructural and mechanical properties of the tricuspid leaflets have mechanobiologically evolved to optimally support their function under those forces. Yet, how the tricuspid leaflet microstructure determines its mechanical properties and whether this relationship differs between the three leaflets is unknown. Here we perform a microstructural and mechanical analysis in matched ovine tricuspid leaflet samples. We found that the microstructure and mechanical properties vary among the three tricuspid leaflets in sheep. Specifically, we found that tricuspid leaflet composition, collagen orientation, and valve cell nuclear morphology are spatially heterogeneous and vary across leaflet type. Furthermore, under biaxial tension the leaflets' mechanical behaviors exhibited unequal degrees of mechanical anisotropy. Most importantly, we found that the septal leaflet was stiffer in the radial direction and not the circumferential direction as with the other two leaflets. The differences we observed in leaflet microstructure coincide with the varying biaxial mechanics among leaflets. Our results demonstrate the structure-function relationship for each leaflet in the tricuspid valve. We anticipate our results to be vital toward developing more accurate, leaflet-specific tricuspid valve computational models. Furthermore, our results may be clinically important, informing differential surgical treatments of the tricuspid valve leaflets. Finally, the identified structure-function relationships may provide insight into the homeostatic and remodeling potential of valvular cells in altered mechanical environments, such as in diseased or repaired tricuspid valves.

Quenching and partitioning (Q&P) steel plays a significant role in automotive lightweighting on the merits of high strength and good ductility. Yield behavior of Q&P steels with strength grades of 1180 MPa (QP1180) and 980 MPa (QP980) and one dual-phase steel (DP980) were characterized under various proportional loading, i.e., uniaxial tension, uniaxial compression, simple shear and biaxial tension utilizing cruciforms with arms reinforced by laser deposition, i.e., an additive manufacturing process. Results show that QP1180 and QP980 exhibit pronounced strain hardening, strength differential effect and anisotropic hardening rather than DP980. The Karafillis and Boyce (1993) yield criterion was modified and further employed to construct a multiplicative yield criterion under non-associated flow rule. Anisotropic hardening is captured by directly employing the stress vs. strain curves under uniaxial tension, uniaxial compression and equi-biaxial tension. Besides, a user-friendly calibration strategy was proposed to identify the shape-dominating parameters in the developed yield criterion utilizing the flow stresses under plane strain and simple shear. Finally, evolving asymmetric yield surfaces of the two investigated Q&P steels were accurately described by the developed yield criterion.

The plastic deformation behavior under various strain-path changes in an A6022-T4 Al alloy sheet was studied, focusing on the evolution of the direction of the plastic strain rate θ and the stress ratio φ after abrupt strain-path changes. A cruciform specimen was used to measure the evolution of the plastic deformation behavior after abrupt strain-path change experimentally. Before the strain-path change, the deformation was represented well by the associated flow rule with the Yld2000-2d yield function and isotropic hardening assumption. After the abrupt-path change, the deformation temporarily deviated from the associated flow rule, and it could be represented again by the associated flow rule after the plastic work increased roughly 4.0 MJ ⋅ m − 3 , which corresponded to the strain increment of approximately 0.024 under uniaxial tension in the rolling direction. The transitions of θ and φ as a function of plastic work showed that both θ and φ tend to converge to certain values regardless of the strain path if the final strain-path angles are identical. It was also found that the relationships between φ and θ temporarily deviate from the associated flow rule immediately after the abrupt-path changes because φ cannot follow the rapid change of θ . Crystal plasticity finite-element simulations reproduced the qualitative tendencies observed in the experiments, but the deviations from the associated flow rule were much more pronounced. Parametric studies showed that φ tends to converge to different values depending on the strain rate sensitivity, whereas θ tends to converge to a same value irrespective of the rate sensitivity exponent. The rate sensitivity exponent m = 0.044 gave the best fits with the experimental results in terms of the evolution of both θ and φ under an abrupt-change path, although the rate sensitivity exponent determined from macroscopic strass-strain curves were m = 0.002.

Using density functional perturbation theory (DFPT) with Born effective charges included, we calculate in detail the phonons of bulk and monolayer HfS2. Our calculated phonon frequencies and LO–TO splitting agree well with experimental data. The variation of phonon frequencies from bulk to monolayer can be accounted for in terms of the delicate balance of the long- and short-range force constants. The ultimate strength under biaxial tensile strain is explored for the first time. Monolayer HfS2 can suffer only no more than 6% tensile strain. Our important finding is that the phonon gap appears when goes to single layer from bulk and can be tuned by biaxial tension. By analysing the Eliashberg function we conclude that HfS2 cannot turn to superconductivity by electron–phonon interaction.

A good knowledge of forming limits at fracture (FLF) for aluminum sheets exhibiting poor formability at room temperature in various non-linear strain paths (N-LSPs) is essential for fully exploiting their forming ability and avoiding their fracture failure. However, the FLF over a wide range of strain states in N-LSPs with pre-strain paths between uniaxial tension and simple shear cannot be determined through the existing two-stage loading test methods. To solve the problem and fill the gap, a new two-stage loading test method employing an optimized butterfly specimen is proposed in this paper, in which strain path changes are controlled by changing biaxial loading conditions acting on the specimen. To validate the capability of the new test method to characterize the FLF in the N-LSPs and investigate the effect of the loading path changes on aluminum 6K21-T4 sheet formability at fracture, different proportional and non-proportional loading experiments using the butterfly specimen obtained from the aluminum sheets are performed. Experimental results indicate that the forming limit strains at fracture over a wide scope of strain states in the N-LSPs can be effectively determined by utilizing the proposed method, thus filling the gap mentioned above. Additionally, four newly developed ductile fracture criteria (a new model proposed in this paper, Hu−Chen 2017, Lou−Huh 2012 and MMC3) together with a non-linear damage accumulation rule (N-LDAR) are employed to forecast the FLF for the 6K21-T4 sheets in the N-LSPs. The results show that both the proposed new model with the N-LDAR and the Hu−Chen model along with the N-LDAR can provide the highest prediction accuracy for the FLF in the N-LSPs. However, the prediction accuracy of the proposed model is much higher that of the Hu−Chen 2017 model for aluminum alloy 5083-O sheets.

Although { 10 1 ¯ 2 } twinning behavior has been extensively studied, it has rarely been investigated under biaxial tension. In the present research, the mechanical response and { 10 1 ¯ 2 } twinning behavior of a Mg AZ31 sheet under biaxial tension with various stress ratios ( σ N D : σ T D ) along the normal direction (ND) and transverse direction (TD) were systematically studied. The results indicate that the yield stress along the ND is nearly independent of σ N D : σ T D . Schmid law applied to { 10 1 ¯ 2 } twinning under biaxial tension yields better efficiency than that for uniaxial tension, and a higher efficiency is observed with a larger stress ratio along the TD; the fraction of experimentally observed twin variants with Schmid factors (SFs) of ranks 1 and 2 is approximately 45% for uniaxial tension, whereas it is approximately 68% for σ N D : σ T D = 2 : 1 and approximately 88% for σ N D : σ T D = 1 : 2 . This result contradicts with the previously reported result that Schmid law is more efficient for uniaxial stress states than under multiaxial stress conditions. It is found that biaxial tension will increase the difference in SF for the six twin variants and make Schmid law more efficient. Twin variant selection and volume fraction are highly dependent on σ N D : σ T D . For uniaxial tension, the activities for the six variants are similar, and the (0002) poles of the twins are distributed evenly on a circle approximately 80°–90° away from the ND. In contrast, the variants ( 0 1 ¯ 12 ) [ 01 1 ¯ 1 ] and ( 01 1 ¯ 2 ) [ 0 1 ¯ 11 ] are more favorable under biaxial tension, and more (0002) poles of the twins concentrate around the rolling direction with a higher ratio of σ T D . At a similar strain level, the twin fraction under biaxial tension is often different from that under uniaxial tension, and this difference varies with σ N D : σ T D . This mechanism is associated with a stress-ratio-mediated detwinning behavior under biaxial tension. The findings in the present study provide a new and significant understanding of the twinning behavior of Mg alloys.

This work investigates the influence of equi-biaxial stress state on the deformation response of Ti-6Al-4V alloy in mill-annealed condition using a newly designed cruciform specimen geometry. The proposed geometry was validated using a non-contact strain measurement technique to obtain maximum plastic strain in the gage section. It is observed that the elasto-plastic response of Ti-6Al-4V alloy was profoundly influenced by the stress state and the loading orientation with respect to the rolling direction. The strengthening effect and the in-plane plastic anisotropic evolution observed under equi-biaxial stress state was ascribed to the presence of strong crystallographic texture in the as-received condition. The dominant deformation mechanisms operating under equi-biaxial stress state were deduced from the texture evolution studies.

Steel-Concrete-Steel (SCS) composite wall is being used for different purposes for its improved performances. Some analytical and finite element models have been presented in the past to predict the behavior of such walls. In this paper, an attempt is made to develop an iterative membrane model to analyze SCS wall panels subjected to in-plane membrane forces in the principal directions. The model accounts for the post-cracking Poisson effects of concrete as the Zhu/Hsu ratio. Individual behaviors of concrete and steel plates in an SCS panel are studied in which confinement in principal tensile direction accompanied by negative uniaxial tensile strain in concrete is observed. To explain this behavior, a detailed perspective for uniaxial strain in principal tensile direction is proposed and the conventional stress-strain trajectory of concrete in tension is extended to incorporate any confinement developed in the concrete. Constitutive law of concrete in compression is also modified to incorporate the observed confining behavior of the concrete.

A new phenomenological ductile fracture criterion that is proposed. The proposed model is associated with the micro mechanisms of void nucleation, void growth, and evolution of void coalescence. The secondary voids band and rotation of voids effect are considered in the new ductile fracture criterion. A series of upsetting test results of aluminum 2024-T351 and TRIP RA-K40/70 steel are used to construct and compare the accuracy of fracture locus proposed by new ductile fracture criterion, Modified Mohr-Coulomb criterion and extend Lou-Huh criterion. The fracture locus constructed using the proposed criterion is close to the experimental data points over a wide stress state range from uniaxial compression to balanced biaxial tension. Then, a series of upsetting tests and square cup drawing tests are conducted with Al6014-T4 to evaluate the accuracy of the proposed criterion. All results indicate that the proposed ductile fracture criterion can be utilized for predicting initial fracture in sheet metal forming.

Using atomistic simulations and dislocation theory on a model system of semi-coherent {1 1 1} interfaces, it is shown that misfit dislocation nodes adopt multiple atomic arrangements corresponding to the creation and redistribution of excess volume at the nodes. Four distinctive node structures were identified: volume-smeared nodes with (i) spiral or (ii) straight dislocation patterns, and volume-condensed nodes with (iii) triangular or (iv) hexagonal dislocation patterns. Volume-smeared nodes contain interfacial dislocations lying in the Cu–Ni interface but volume-condensed nodes contain two sets of interfacial dislocations in the two adjacent interfaces and jogs across the atomic layer between the two adjacent interfaces. Under biaxial tension/compression applied parallel to the interface, it is shown that the nucleation of lattice dislocations is preferred at the nodes and is correlated with the reduction of excess volume at the nodes.

Part I of this paper showed that under biaxial tension–compression load the energy dissipation capacity of fibre reinforced concretes (FRC) is up to 30% lower than under uniaxial tension load. In this part, the extent of the fracture process zone (FPZ) was studied with the acoustic emission technique and the decrease of the energy dissipation will be explained. It was found that plain concrete specimens have generally narrower/smaller FPZ compared to FRC specimens under both uniaxial tension and biaxial tension–compression load case. Under biaxial tension–compression load for both unreinforced and fibre reinforced specimens the FPZ tends to become slightly wider compared to the uniaxial tension load case. However with increasing biaxial compression stress ratios the specimens energy absorption capacity decreases. In case of biaxial load, the bond between the fibre and the matrix zone is affected by the lateral compression stresses, resulting in a smaller FPZ compared to the uniaxial load. This is believed to be the main reason for the lower dissipated energy.

Within each of the four layers of mitral valve (MV) leaflet tissues there resides a heterogeneous population of interstitial cells that maintain the structural integrity of the MV tissue via protein biosynthesis and enzymatic degradation. There is increasing evidence that tissue stress-induced MV interstitial cell (MVIC) deformations can have deleterious effects on their biosynthetic states that are potentially related to the reduction of tissue-level maintenance and to subsequent organ-level failure. To better understand the interrelationships between tissue-level loading and cellular responses, we developed the following integrated experimental-computational approach. Since in-vivo cellular deformations are not directly measurable, we quantified the in-situ layer-specific MVIC deformations for each of the four layers under a controlled biaxial tension loading device coupled to multi-photon microscopy. Next, we explored the interrelationship between the MVIC stiffness and deformation to layer-specific tissue mechanical and structural properties using a macro-micro finite element computational model. Experimental results indicated that the MVICs in the fibrosa and ventricularis layers deformed significantly more than those in the atrialis and spongiosa layers, reaching a nucleus aspect ratio of 3.3 under an estimated maximum physiological tension of 150 N/m. The simulated MVIC moduli for the four layers were found to be all within a narrow range of 4.71–5.35 kPa, suggesting that MVIC deformation is primarily controlled by each tissue layer’s respective structure and mechanical behavior rather than the intrinsic MVIC stiffness. This novel result further suggests that while the MVICs may be phenotypically and biomechanically similar throughout the leaflet, they experience layer-specific mechanical stimulatory inputs due to distinct extracellular matrix architecture and mechanical behaviors of the four MV leaflet tissue layers. This also suggests that MVICs may behave in a layer-specific manner in response to mechanical stimuli in both normal and surgically modified MVs.

Small punch testing is now a widely recognised approach for obtaining useful mechanical property information of critical structural components, particularly in the nuclear industry. However, to date the utilisation of this method has been limited to isotropic materials such as aluminium alloys and steels. This paper will look to utilise the small punch (SP) test to assess the creep response of 〈001〉-orientated CMSX-4 1 at temperatures above 950 °C. An orthogonal rafting regime of the γ′ structure is observed in the post-test microstructure due to the biaxial tension state typically produced in a SP test. Interpretation of the SP results to correlate with uniaxial creep data is carried out by employing the k sp approach in order to provide a platform for future material assessment.

Crack growth behavior of aluminum alloy 7075-T6 was investigated under in-plane biaxial tension–tension fatigue with stress ratio of 0.5. Two biaxiality ratios, λ (=1 and 1.5) were used. Cruciform specimens with a center hole, having a notch at 45° to the specimen’s arms, were tested in a biaxial fatigue test machine. Crack initiated and propagated coplanar with the notch for λ = 1 in L–T orientation, while it was non-coplanar for λ = 1.5 between L–T and T–L orientations. Uniaxial fatigue crack growth tests in L–T and T–L orientations were also conducted. Crack growth rate in region II was practically the same for biaxial fatigue with λ = 1 in L–T orientation and for the uniaxial fatigue in L–T or T–L orientations, while it was faster for biaxial fatigue with λ = 1.5 at a given crack driving force. However, fatigue damage mechanisms were quite different in each case. In region I, crack driving force at a given crack growth rate was smallest for biaxial fatigue with λ = 1.5 and for uniaxial fatigue in T–L orientation, followed by biaxial fatigue with λ = 1 and uniaxial fatigue in L–T orientation in ascending order at a given crack growth rate.

A simple model system using synthetic materials was developed to simulate the in vivo mechanical behavior of prosthetic meshes. Two types of prosthetic meshes, SPMM (heavy-weight) and Gynemesh M (light-weight, partly absorbable) were embedded in dry conditions in an elastomeric matrix. These composites were characterized using two different testing configurations, i.e., uniaxial and biaxial tension. Stiffness parameters were calculated from the non-linear membrane tension versus stretch curves at different levels of membrane tension. The present model system qualitatively reproduces and even clarifies – as it is not affected by biological scatter – the findings of an analogous animal study (full thickness abdominal wall defect rabbit model). Biaxial tangent moduli are higher for SPMM than for Gynemesh M . A ranking of meshes according to uniaxial tangent moduli depends on the load level. At low tensions SPMM is stiffer than Gynemesh M , at moderate levels SPMM is more compliant than Gynemesh M . Stiffness values of meshes ingrown in native rabbit abdominal wall tissue are quantitatively determined based on data from the present protocol. Experiments using mesh elastomer composites were qualified as an effective tool for a mechanical characterization of prosthetic meshes. They are useful for an engineering optimization of textile meshes before a final validation in animal studies.

PSA Peugeot Citroen uses for many year the Dang Van criterion for cylinder head high cycle fatigue design. If this well-known criterion is very efficient for a large number of solicitations, tests on engine bench showed it is very conservative for local stress state corresponding to biaxial tension with high mean stress. An experimental campaign conducted in collaboration with the LAMPA (Laboratoire Arts et Metiers ParisTech d’Angers), focused on equi-biaxial tensile tests, confirmed the inability of the Dang Van criterion to estimate the correct fatigue strength for such loadings. An empirical criterion was developed, based on the modification of one parameter of the Dang Van criterion with respect to the biaxiality rate and to the load ratio. This criterion was successfully tested on an important number of biaxial fatigue tests from the literature and on cylinder head simulations.

Biaxial tensile tests of 6000 series aluminum alloy sheet with different density cube textures were conducted using cruciform specimens. The specimens were loaded under linear stress paths in a servo-controlled biaxial tensile testing machine. The plastic orthotropy remained coaxial with the principal stresses throughout every experiment. Successive contours of plastic work in stress space and the directions of plastic strain rates were precisely measured and compared with those calculated using selected yield functions. The Yld2000-2d yield functions with exponents of 12 and 6 were capable of reproducing the general work contour trends and the directions of plastic strain rates observed for the test materials with high and low density cube textures, respectively. Hydraulic bulge tests were also conducted and the variation of thickness strain along the meridian directions of the bulged specimen was compared with that calculated using finite element analysis (FEA) based on selected yield functions. Differences in the cube texture density caused significant differences in the strain distribution of the bulged specimens, and were in good agreement with the FEA results obtained using the Yld2000-2d yield functions. It is thus concluded that the biaxial tensile testing method with a cruciform specimen is an effective material testing method for accurately detecting and modeling the deformation behavior of sheet metals under biaxial tension.

Deformability of a single-ply E-glass non-crimp 3D orthogonal woven reinforcement (commercialized under trademark 3WEAVE® by 3Tex Inc.) is experimentally investigated. The study is focused on the understanding and measurement of the main deformation modes, tension and in plane shear, which are involved during draping of composite reinforcements by: (i) uniaxial and biaxial tension; (ii) in-plane shear investigation using uniaxial bias extension and picture frame tests; and (iii) measurements of the fabric thickness variation during shear. The test methods common for 2D fabrics are validated for the thick 3D reinforcement. The obtained results represent a data set for the simulation of a forming process with the 3D reinforcement.

In this paper, yield locus was measured for Ni3Al-based intermetallic alloy sheet samples, which were directionally solidified in [0 0 1] orientation. The yielding behavior was measured in both biaxial tension and biaxial compression. Significant anisotropy and yielding asymmetry between tension and compression were found. In order to model the complex yield behavior of the Ni3Al-based alloy, a new yield criterion has been proposed, which is based on the one given by Barlat and Lian. Finally, the predictions of the new criterion and several other existing yield criteria were compared to the experiment data. Results show that the new yield criterion can predict both the anisotropy and yielding asymmetry of the alloy with good accuracy, whereas other criteria lead to significantly discrepancies in biaxial compression region. Therefore, the new criterion can be used to study, at a low degree of complexity, the complicated yielding behavior of Ni3Al-based intermetallic alloys.

The current study aims to show the benefits of dispersed laminates (laminates in which the orientation angles are not limited to the conventional, 0°, ±45° and 90°, orientations) over conventional ones, in terms of stiffness, buckling resistance and strength, in structural applications. The Ant Colony Optimization algorithm is used with strength constraints to find the best candidate to achieve this goal. A study is conducted to select the most suitable failure criterion among three common ones. The methodology is used for two loading cases: biaxial compression and biaxial tension. In the case of biaxial compression, the problem is formulated to maximize the critical buckling load whereas with the biaxial tension, the formulation is to minimize the failure index. For both loading cases, the methodology succeeds in improving the response of dispersed laminates with respect to the conventional ones. These results support the movement of the composite industry toward using dispersed laminates.

The development of texture during plastic deformation plays an important role in determining the stretch formability of magnesium alloy sheets. In this study, the orientation stability during equibiaxial tension of magnesium was analyzed based on three dimensional lattice rotations calculated by using a rate-dependent crystal plasticity model and assuming five different combinations of slip modes. The results show that no orientations can satisfy the stability criteria with both zero rotation velocity and convergent orientation flow in all dimensions. However, relatively stable orientations with zero rotation velocity and an overall convergence are found. They are featured by characteristic alignments of specific crystallographic directions in the macroscopic axis of contraction, depending on the slip modes involved in the deformation. It is also shown that the orientation stability varies significantly with the deviation of deformation mode from equibiaxial tension. The simulation results are briefly discussed in comparison with pre-existing experiments.

We perform two-dimensional dynamic fracture simulations of a specimen in biaxial tension, incorporating various distributions of pre-existing microcracks. The simulations consider the spatial distribution of flaws while modeling the discrete failure processes of crack interactions and coalescence, and predict the macroscopic variability in failure strength. The model quantitatively predicts the effect (on the dynamic failure strength) of different shapes of the flaw size distribution function, the random spatial distribution of flaws, and the random local resistance to crack growth (i.e. strength) associated with each flaw. The effect of changing material volumes on the variability in failure strengths is also examined in relation to the flaw size distribution. The effect of loading rate on the variability in failure strengths is presented in a form that will enable improved constitutive modeling using non-local formulations at the continuum scale. (C) 2010 Elsevier Ltd. All rights reserved.

This paper presents a new method to determine the crack-tip plastic zone size ( R y ) in the center cracked plate in tension. The maximum crack opening displacement (MCOD) is used to estimate R y in this method. Based on the series of calculation results by finite element analysis, the explicit expression for the crack-tip plastic zone size versus MCOD is fitted by least square method. The expression enables to eliminate the influences of the yield stress of material, crack geometry, plate sizes and transverse stress. Therefore, the presented method of R y determined by MCOD is suitable to any center crack finite plate of any material under uniaxial or biaxial tension.

Stress intensity factors of thin AZ31B magnesium alloy sheet under biaxial tension loading were analyzed by modified Dugdale model. K-values with crack angle of 90° obviously show that there is no influence of the loading condition in Mode-I. In the 45° case, KI values are obtained within 10% errors when they are calculated by modified Dugdale model under biaxial loading. It is concluded that the modified Dugdale model is one of effective ways to evaluate stress intensity factor of AZ31 magnesium alloy sheet appropriately.

The mechanical relation of isotropic three-dimensional reticulated porous metal foams with stochastic pores is investigated under complex loads of triaxial tension and compression. From the simplified structural model, the mathematical relationship between three nominal main stresses and porosity has been derived for this class of porous materials at failure under the above-mentioned complex loads, covering three loading conditions of biaxial tension with monoaxial compression, of biaxial compression with monoaxial tension, and of triaxial compression. Through the relevant expression from the deduction, the criterion of strength design can be further obtained for these porous materials under these multiaxial complex loadings.

The deformation behaviour and structural evolution of bulk metallic glass sheets were studied under biaxial tension in supercooled liquid state. The sheets were gas pressure formed into hemispherical and semi-ellipsoid domes using dies with aspect ratios of 1:1 and 3:2, respectively, at the optimum temperature of 676 K. The structural evolution of the metallic glass sheets was examined after deformation. The stress distributions of the bulging sheets are calculated employing a finite element model. It was found that the stress state of biaxial tension accelerates nanocrystallization, which leads to an increase in the hardness of metallic glass. The gas pressure applied, bulging time, and temperature are the principal factors involved in the formation of products.

The biaxial creep damage of type 304 stainless steel is studied at 973 K. Biaxial tension creep tests were carried out using cruciform specimens under the principal stress ratio ( λ ) of 0 ≦ λ ≦ 1, where the principal stress ratio is the ratio of y -directional principal stress to x -directional stress in the gage part of the specimen ( λ = σ y / σ x ). Creep rupture times under biaxial stress conditions were shorter than those in uniaxial conditions at the same von Mises equivalent stress. Earlier void nucleation and faster void growth were observed in creep tests at larger principal stress ratio tests. Creep rupture times in biaxial stress states were discussed in relation to the void observations.

In this work, we are interested in the study of the mechanical behavior of the elastomers materials. We analyze mainly their ultimate properties. This study is based on the first Seth strain measures invariant [1] and the literature experimental data [2] , [3] , allowing to take into account of the multiaxial loading effects. With this intention, the step that we adopted is translated by the division of this work into two parts: In the first time, we developed the relation of Seth–Hill based to the strain measures. In the second time, we exposed the principal experimental results used in this work, including versus loading modes (uniaxial tension, equal biaxial tension and biaxial tension), realized on two types of elastomers: a natural rubber (NR) and a styrene butadiene rubber (SBR). Indeed, the installation the first invariant of the Seth strain measures and the experimental results data made it possible to obtain an exploitable data base to determine the non-linear evolution of elastomers behavior at rupture in order to identify its parameter’s materials after.

Magnesium alloys usually exhibit low ductility at the room temperature due to its hexagonal close-packed structure, but it will be improved at elevated temperature. Therefore, warm press-forming of magnesium alloy sheets is quite attractive. In order to determine the optimum condition of press-forming for magnesium alloy sheets, in the present work, the effects of strain rate, temperature and sheet thickness on the yield locus were experimentally investigated. The yield loci of magnesium alloy (AZ31) sheets with different sheet thickness (0.5 and 0.8 mm) were obtained by performing biaxial tensile tests, using cruciform specimens, at temperatures of 100, 150, 200, 250 and 300 °C at strain rates of 10 −2 , 10 −3 and 10 −4 s −1 . Based on the experimental results, the effects of strain rate, temperature and sheet thickness on the yield locus were discussed. The size of yield locus drastically decreases with increasing temperature and decreases with decreasing strain rate. In contrast with the temperature and strain-rate dependence of the yield locus, sheet thickness has no influence on the yield locus. The shape of the yield locus of magnesium sheet is far from the predictions calculated by the yield functions of von Mises, Hill and Cazacu. Instead of these, the yield functions of Logan-Hosford or Barlat is a better choice for the accurate description of biaxial tension stress–strain responses at high temperature.

In the present paper, an infinite face-centered cubic single crystal containing an isolated cylindrical micron-sized void, which is subjected to proportional and monotonically uniform equal biaxial tension loading, is adopted to study the scale-dependent void growth and its intrinsic mechanism by employing a two-dimensional planar discrete dislocation dynamic framework. First, a typical dislocation distribution near the microvoid is presented and the void growth mechanism is revealed by dislocation shear loop expansion for each of three typical fcc slip systems. The effect of size on void growth is then investigated. The general conclusion that voids at the micron or submicron scale are less susceptible to growth than larger ones is drawn. Another result, which cannot be deduced from the continuum theories, is also achieved: at the micron or submicron scale, larger voids grow smoothly with remote strain, while smaller voids usually grow in a “leapfrog” manner. Specifically, when the void is even smaller, it grows in an approximately linear-elastic manner since only few dislocations are present around the void. Further analyses indicate that these size effects are closely related to the dislocation density on the void surface and the dislocation mobility around the void. Finally, the influences of the dislocation sources/obstacles density and their random distribution in materials on the void growth are studied briefly. Results show that there exists remarkable scatter in the microvoid growth due to random distribution of the dislocation sources or obstacles, especially for voids at the submicron scale. These results are helpful for us in understanding the size-dependent damage mechanism at the micron or submicron scale.

Foamed metals have been widely used as various engineering materials, and their mechanical properties have also been drawing extensive attention. In the present paper, a new mechanical and analytical model is established for these materials with isotropic three-dimensional reticulated structure under biaxial tension, and the mathematical equation about biaxial nominal stresses is deduced for the biaxial tension at the beginning of failure of the porous body. With the relevant experiment, the relation formula is proved to be very effective. Different from the relevant theoretical system of Gibson and Ashby, the present mathematical relationship can be conveniently achieved from directly using the “beam theory” on this mechanical and analytical model. In addition, this relationship can be further expressed as the mathematical relationship among the nominal failure “deviatoric stress”, the nominal failure “average stress” and porosity, but the concepts of both the “deviatoric stress” and the “average stress” can appear just from the mathematical treatment.

In this paper, surface cracked plates under biaxial tension are studied. Three-dimensional elastic–plastic finite element analyses have been carried out to calculate the J -integral for surface cracked plate for a wide range of geometry, biaxiality and material properties. Fully plastic J -integral solutions along the front of the surface cracks are presented for Ramberg–Osgood power law hardening material of n = 3, 5, 10 and 15. Geometries considered are a / c = 0.2, 1.0 and a / t = 0.2, 0.4, 0.6 and 0.8 and the biaxial ratios of 0, 0.5 and 1. Based on these results, the J -integral along the crack front for general elastic–plastic loading conditions can be estimated using the EPRI scheme. These solutions are suitable for fracture analyses for surface cracked plates under biaxial loading.

To decide between clearly different approaches for engineering assessment of plane stress tearing, we performed uniaxial and biaxial tensile tests on middle-cracked specimens at various in-plane constraint states. Attention was focused on determination of the crack tip opening spacing δn, crack tip opening angle ψc, crack mouth opening angle αs, energy dissipation rate R, and specific work of fracture As. Our experimental results demonstrate that the values of δn, ψc, αs, R, and As for a high-strength low-hardening aluminium alloy all depend on the specimen geometry, its size, and the load biaxiality ratio. However, assessment of ductile tearing by interconnected characteristic quantities αs and As is more preferable over the use of δn, ψc, and R values for a number of basically important reasons discussed in this paper.

In times of growing claims for light weight solutions in the transportation industry new materials are required. Especially, high strength steels and light weight materials, e.g. aluminium and magnesium, offer great potentials. Since the behaviour of new materials cannot be predicted, basic investigations have to be done. This paper introduces a kind of specimen which is used for a novel experimental set-up to characterise sheet metals also at elevated temperatures as it is needed for magnesium sheets. Analytical and numerical investigations are done to enhance the fundamental understanding of stress distribution during loading. Optimisation of specimen's geometry is based on FE-calculation and leads to special designed slitted sheets.

The accuracy of defect assessment methods is directly related to the accurate estimation of the limit load of the analyzed defective component. This paper provides closed form solutions of square plates with an elliptical defect subjected to uniaxial and biaxial tension. The defect is assumed to be located in the center of the plate. Lower and upper bounds to the external loads are determined for all parameters of the elliptical defect compared to the length of the side of the plate. Comparisons with the results from detailed finite element limit analyses show good agreement.

The recently developed European flaw assessment procedure SINTAP has been applied to 29 thin sheets made of five different materials and loaded in tension, bending and biaxial tension. Based on these data the analytical SINTAP assessment levels are evaluated with respect of their ability to predict the failure loads as well as stable crack extension behaviour.

To provide biaxial failure behavior characteristics of concrete of a standard Korean nuclear containment building, the concrete specimens with the dimensions of 200 mm ×200 mm ×60 mm were tested under different biaxial load combinations. The specimens were subjected to biaxial load combinations covering the three regions of compression–compression, compression–tension, and tension–tension. To avoid a confining effect due to friction in the boundary surface between the concrete specimen and the loading platen, the loading platens with Teflon pads were used. The principal deformations in the specimens were recorded, and the failure modes along with each stress ratio were examined. Based on the strength data, the biaxial ultimate strength envelopes were developed and the biaxial stress–strain responses in three different biaxial loading regions were plotted. The test results indicated that the concrete strength under equal biaxial compression, f 1 = f 2 , is higher by about 17% on the average than that under the uniaxial compression and the concrete strength under biaxial tension is almost independent of the stress ratio and is similar to that under the uniaxial tension.

Concrete structures such as rigid airport pavements are subjected to repeated high-amplitude loads resulting from passing aircraft. The resulting stress-state in concrete is a biaxial combination of compression and tension. It is of interest to understand the response of plain concrete to such loading conditions, which will enable development of realistic material models for implementation in mechanistic pavement design procedures. The objective of this work is to characterize the quasi-static and low-cycle fatigue response of concrete subjected to biaxial stresses in the biaxial tension region, where the principal tensile stress is larger than or equal in magnitude when compared with the principal compressive stress. An experimental investigation of material behavior in the biaxial tension region is conducted. The experimental setup consists of the following test configurations: (a) notched concrete beams tested in three-point bend configuration, and (b) hollow concrete cylinders subjected to torsion. Failure of concrete in the biaxial tension region is shown to be a local phenomenon under quasi-static and fatigue loading, wherein the specimen fails owing to a single crack. The crack propagation is studied using the equivalent elastic crack concept. It is observed that the crack growth rate in constant amplitude fatigue loading exhibits a two-phase process: a deceleration phase followed by an acceleration stage. The crack growth in the acceleration stage is shown to follow Paris law. The model parameters obtained from uniaxial fatigue tests are shown to be sufficient for predicting the considered biaxial fatigue response.

The cavitation behaviour of superplastic alloys has relatively been less examined under biaxial tension, though it has been demonstrated by some researchers that stress state does affect the cavitation behaviour. In this paper, a commercial superplastic Al5083 alloy was investigated under stress ratios of 1, 0.8293, 0.6667, 0.5985 and 0. It is found that at the same effective strain, the amount of cavities under equi-biaxial tension is significantly larger than that under unaxial tension, which is in agreement with the trend of the theoretical predictions. The cavitation data under stress ratios from 1 to 0.5985 are very close and have much overlaps. These results are consistent with the theoretical predictions, as the difference between the predicted cavity growth rates is not significant. It is considered that more effort is required to improve the accuracy of both the experimental measurements and the theoretical predictions.

In this study, the behavior under biaxial tension of two types of glass knitted fabrics, a rib and a milano weft knit, was investigated. The tests were performed using a homemade biaxial tester, which is capable of applying displacement velocity in two orthogonal directions independently. The ultimate deformation in both wale and course directions was determined at different displacement ratios. Furthermore, geometrical models were developed for the rib knit to predict the ultimate deformation. Good agreement with experimental results was achieved.

This paper presents a theoretical analysis of strength size effect associated with the length and thickness of laminated composites. The presented expressions for prediction of the reliability use the Equal Load Sharing Rule (ELS Rule) and are determined by sequential multi-step failure of single lamina or sublaminate. The developed equations show the influence of the thickness and length on the strength of laminated composites. Strength size effect of unidirectional laminated composite under uniaxial tension, and cross-ply laminated composite under biaxial tension is analyzed and presented. The numerical results show the difference between size effect associated with length and that with thickness. Therefore, if Weibull weakest link model is used to predict strength size effect associated with the length and thickness of laminated composites, modification should be introduced.