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An experimental investigation is performed to investigate the effect of post-processing heat treatment on the interfacial fracture toughness of bi-material additively manufactured semi-crystalline polymer composite. An asymmetric double cantilever beam (ADCB) and single-leg bending (SLB) specimens made of polylactic acid (PLA) and Nylon are considered for the mode-I and mixed-mode fracture characterization, respectively. Specimens are isothermally heated in a forced convection oven for a wide range of temperatures and durations. Fracture toughness decreases significantly for both mode-I and mixed-mode conditions when specimens are annealed below the melting temperature of PLA (150 °C). An increase of the crystallinity at the high-temperature annealing prevents the polymer chain mobility, hinders the neck growth, and provides poor intermolecular diffusion resulting in decrease of fracture toughness by 88% as compared to the unannealed specimen. Annealing at 160 °C improves the bi-material interfacial fracture toughness by a maximum of 1225% via sufficient interfacial wetting, higher molecular diffusion, and a longer polymer chain entanglement process. Material transfer, void collapse, and filament impression on the fracture surface of high temperature annealed specimen indicate a better molecular diffusion and strong interlaminar bond at the interface.

An experimental study is performed to investigate the dynamic fracture of additive manufactured Acrylonitrile Butadiene Styrene (ABS). A single edge notched bending (SENB) specimen with three orientations, namely horizontal builds with 45°/−45° (H45), 0°/90° (H90) raster orientations, and vertical builds with layers perpendicular to the pre-crack (V0) are considered for this study. In addition, a novel toughening mechanism is explored by changing the surface topology to deflect the crack paths. A modified split Hopkinson pressure bar with a copper pulse shaper (to increase the raising time of incident loading pulse) is used to conduct a three-point bend impact experiment to characterize the dynamic fracture initiation toughness and crack dynamics of 3D printed specimens. Real-time crack initiation and propagation is captured by using a high-speed video camera. Using the load history diagram, accurate fracture initiation load is found to determine dynamic fracture initiation toughness. Fracture initiation toughness is increased by 138% for a V0 specimen configuration compared to H90. Three different sized circular patterns (with diameters of 1, 1.75 and 2.5 mm) and a square pattern (with a length of 1.53 mm) are considered to observe the effect of surface topology on the dynamic fracture initiation toughness. Introducing surface pattern to the specimen increases the fracture toughness by 58% as compared to specimens without surface pattern. Surface pattern also exhibits two steps of crack growth and decreases the initial crack propagation velocity significantly for all three orientations. Additionally, higher fracture initiation toughness is achieved with the increase in the size of the pattern and the change of the pattern shape.

A custom designed dynamic mechanical apparatus was constructed to measure the tan(δ) (loss tangent) properties of Flocked (layer) Energy Absorbing Materials (FEAM). Flocked Impact Energy Absorbing (IEA) materials derive their dynamic mechanical impact absorbing properties from the compressional deformation (bending , buckling) and inter-fiber friction of nominally upright flocked fibers in the flock fiber composite assembly. The reported work summarizes the dynamic mechanical, low strain, linear viscoelastic tan(δ) properties of FEAM composite layer structures at frequencies from 25 to 100 Hz and a temperature range of 0 °C–50 °C. The effect of tan(δ) at various flock densities (fibers/mm 2) was also measured. These studies were carried out to gain information and insight into the role that a material’s dynamic mechanical properties have on the overall IEA performance of sport (and military) apparel pad structures. Results show that the tan(δ) of FEAM materials increases as the measuring frequency and flocked layer’s flock density increase. Tan(δ)’s behavior at various temperatures (0 °C–50 °C) did not follow an expected trend; the highest tan(δ) value was observed to occur at room temperature. Nevertheless, the obtained tan(δ) information on these various FEAM configurations should provide some guidance in designing optimized FEAM sport (and military) pad IEA composites.

A combination of computational and experimental investigation is performed to study additively manufactured (AM) polymers for enhanced fracture properties. Single edge notch tension specimens made of acrylonitrile-butadienestyrene (ABS) materials through fused deposition modeling with various build/raster orientations are studied, namely, horizontal builds with 45°/−45° (45–45) or 0°/90° (0–90) raster orientations, and vertical builds with layers perpendicular to the notch (V0). The measured fracture properties were found to highly depend on the build/raster orientations and crack kinking was observed in 45–45 samples to follow the weak inter-filament weld-lines. The extended finite element method (XFEM) using cohesive segment approach with anisotropic damage initiation and evolution criteria was developed to capture the dependency of fracture behaviors on build/raster orientations. Numerical parametric studies further show that the inter-filament bonding strength could be tuned to create alternate crack paths for maximum energy dissipated in AM polymer fracture. Finally, toughening mechanisms using topological patterns on the sample surface to deflect crack paths are demonstrated in experiments. This study sheds light on optimization of AM polymers for enhanced fracture properties.

A comprehensive experimental investigation was performed to study the dynamic compressive constitutive response of novel auxetic Kevlar®/epoxy laminated composites. Strain rate response was investigated using the split Hopkinson pressure bar (SHPB) test setup. Laminated composites were fabricated using the vacuum infusion process. Short Nylon fibers were flocked between the laminates with different flock densities and flock length. For obtaining dynamic force equilibrium in SHPB experiments, a copper pulse shaper was used to increase the rising time of incident pulse. To have a comparison, woven Kevlar®/epoxy composites were also characterized at similar strain rates. In addition, quasi-static tests were also performed on both woven and auxetic laminated composites for completeness of the study. For quasi-static loading conditions, auxetic composites showed higher peak strain and lower peak stress compared to woven composites. For non-flocked composites, both auxetic and woven composites showed rate dependency. Woven composites provided 353% increase in peak stress when the strain rate increased from 1200 s−1 (low) to 3300 s−1 (high). However, in the same conditions, auxetic composites showed only 155% increase in peak stress. For different flocking conditions, woven composites showed rate dependency for all strain rates, but auxetic composites demonstrated rate dependency only from low to medium strain rates. Both auxetic and woven composites experienced shear failure under quasi-static compression, where auxetic composites failed at higher shear angle of 37°, but woven composites had a failure angle of 30°. For impact loads, under no flocking condition, woven composites did undergo severe edge failure at all strain rates, but auxetic composites showed a sign of edge failure only at high strain rates. With the flocking condition, auxetic composites had through thickness shear failure and woven composites experienced splitting and fibrillation of Kevlar® fibers.

A comprehensive experimental investigation was performed to understand damage detection capabilities of intra-ply glass/carbon composites embedded with carbon nanotubes under mode-I and mode-II fracture. Novel modified four circumferential probes were employed on fracture test specimens to capture piezo-electrical response. The effect of three different laminate orientations (G-0-C-90, C-0-G-90, and G-45-C-45) on both mode-I and mode-II fracture initiation toughness and the electrical-fracture response were discussed. C-0-G-90 demonstrated higher mode-I fracture toughness, while G-0-C-90 composites exhibited higher mode-II fracture toughness. The fracture toughness values were related with scanning electron microscopy images and electrical response was correlated well with the crack dynamics.

In this study, a comprehensive experimental investigation is performed to observe the influence of printing process parameters on the interfacial fracture toughness of bi-material additively manufactured composites. A single leg bending (SLB) specimen made of Polylactic acid (PLA) and Nylon is loaded under the quasi-static three-point bending condition to initiate the fracture between the PLA/Nylon interface. Six different process parameters (bed temperature, printing temperature, printing speed, printing orientation, layer height, and thickness ratio) are considered to investigate the fracture toughness. It is observed that process parameters have a significant impact on the bi-material interfacial fracture toughness. Due to the increase of crystallinity of the polymer, the fracture toughness decreases by about 40% when the bed temperature increases from 60 °C to 100 °C. However, with improved molecular diffusion, the fracture toughness is enhanced by 95% with the increase of the printing temperature. Although printing speed has not any significant impact on fracture toughness, thinner layers provide a better bond strength and polymer wetting, resulting in a higher fracture initiation toughness compared to thicker layers. Due to the presence of extra voids and anisotropic behavior, the specimens of 0o/90o raster-orientation demonstrate about 75% lower fracture toughness compared to those of +45o/-45o orientated specimens.

Numerical studies were performed to determine electrical contacts in carbon nanotubes (CNTs)-embedded epoxy under quasi-static tensile loading conditions. A realistic CNT network in epoxy was generated by random orientation and waviness by employing the Monte Carlo method. Two kinds of contacts between CNTs, namely Type-I (overlap) and Type-II (in-plane), were considered in generating a conductive network. A commercial finite element package, COMSOL, was used to determine the distance between these contacts and variation of these contacts during elastic deformation under tensile loading. Numerical predictions were later compared with the analytical results derived from experimental findings. The effect of initial f-ratio and the amount of waviness of CNTs on the variation of f-ratio (which is determined as a ratio of Type-II contacts to total contacts) was investigated as a function of axial strain. The initial f-ratio as well as the extent of waviness showed a significant effect on the change in the type of contacts with increasing axial strain values.

Experimental study was performed to investigate fracture and impact properties of novel Auxetic Kevlar® laminated composites. For comparison, standard Kevlar® woven composites with and without polyurethane treatment were also considered in this study. For these three composites, short nylon fibers of two different fiber lengths and three different fiber densities were flocked between laminates. Vacuum infusion process along with optimized compaction was employed to fabricate composites. The double cantilever beam configuration was used to investigate the fracture properties. The Auxetic Kevlar® composites showed a significant improvement of 225% in fracture toughness compared to regular woven Kevlar® composites. Furthermore, the initiation toughness was increased by 577% with the application of flocking in Auxetic Kevlar®. During impact testing, the Auxetic Kevlar® reinforced composites showed a significant reduction in damaged area compared to woven counterpart. On the other hand, the reduction in damaged area influenced the reduction in impact energy absorption.

Natural fibers are lighter, less expensive, and less abrasive than synthetic fibers such as glass or carbon, and provide a resource that is both renewable and biodegradable. This study uses surface treatments and flock fiber based Z-axis reinforcement technology to improve the strength and fracture toughness properties of natural fiber composites (NFCs), thus increasing their ability to bear loads. The enhancement of performance properties will expand applications of NFCs in industries such as automotive and housing/construction industries. NFCs will also provide a more sustainable, environmentally friendly, and inexpensive structural material alternative over traditional resin reinforced glass or carbon fiber composite materials.

A detailed experimental study was performed on the piezo-resistive damage sensing of novel electrically conductive inter/intra glass/carbon fiber hybrid epoxy laminated composites reinforced with micro carbon fibers along the thickness direction between the laminates using electro-flocking technique. The electrical resistance is determined by four-circumferential probe measurements under tensile and flexure loads. Intralaminar hybrid composites’ mechanical and electrical properties showed a dependency on layup angle, with glass fibers along the loading direction showed the highest initial resistance value (1180 Ω) and ultimate tensile strength (400 MPa). Intra-ply composites with [±45/∓45] layup orientation demonstrated the lowest ultimate tensile strength (57 MPa) and the highest elongation at break (9.7%). Mechanical and electrical properties of interlaminar hybrid composites showed a dependency on the number of carbon fiber laminates. More carbon fiber laminates within the composite layup produces a lower initial resistance value (0.37 Ω) and higher ultimate tensile strength (247 MPa). In both intra and inter composites cases, with the addition of short carbon fibers, the initial resistance decreased. In some cases, with the addition of short carbon fibers the failure mechanisms changed. Composites of all types experienced much higher percentage change in resistance under flexural loading due to severe interlaminar failure compared to corresponding cases under tensile loading conditions. These results are useful for designing composite structures with emphasis on structural health monitoring.

Damage monitoring of conductive glass fiber/epoxy laminated composites is performed by observing the electro-fracture response under dynamic mixed-mode fracture loading. A three-dimensional conductive network is generated in these composites by embedding carbon nanotubes (CNTs) in the matrix and reinforcing short carbon fibers (80 µm, 150 µm, and 350 µm) between the laminates. A modified split Hopkinson pressure bar setup is used to load the mixed-mode open notch flexure (MONF) specimens. A modified four-point probe technique coupled with a high-frequency data acquisition system is employed to capture the electrical response within process zone of the fracture specimens. A high speed video camera is used to capture the dynamic crack propagation. Due to the bending effect, a decreasing trend in resistance change is observed before the damage initiation in composites with no carbon fibers. However, short carbon fiber reinforced composites show a minimal change in resistance before the crack initiation due to less amount of CNTs in them and moreover short carbon fibers did not change their position during elastic deformation. After crack initiation, the rate of increase of resistance is almost five times higher in composites containing short carbon fibers of 80 µm than to those of 150 µm.

In this study, an experimental investigation is performed to observe the electromechanical response of CB (carbon black)/Acrylonitrile butadiene styrene (ABS) additive manufactured composite under quasi-static (tensile, shear, and mode-I fracture) and dynamic (mode-I fracture) loading conditions for the potential damage sensing applications. Dog bone tensile, double v-notch shear, and single edge notch bending (SENB) specimen printed with three different configurations (0°/90°, +45°/-45°, and 0°) are considered for the quasi-static condition. A modified split Hopkinson pressure bar along with high-speed video camera is used for dynamic fracture experiments. Four-point probe technique coupled with a high-resolution data acquisition system is employed to obtain the real-time electrical response. In the case of tensile loading, +45°/-45° printed specimens show a nonlinear change of electrical resistance due to unique failure mode. Under the shear loading, electrical resistance remains unchanged during the elastic deformation. After the damage evolution, +45°/-45° printed specimens exhibit a higher rate of change in electrical resistance due to alignment of the filaments along the maximum principle shear stress direction. For both static and dynamic fracture loading, a minimal change of electrical resistance is observed before crack initiation. However, after the crack initiation, a sharp change of electrical resistance for 0°/90° printed specimens indicates a faster crack propagation as compared to the +45°/-45° printed specimens.

Theoretical modeling and experimental validation for electro-shear behavior of carbon nanotubes (CNTs) embedded epoxy under quasi-static shear loading are performed. The theoretical modeling incorporates electron tunneling between CNTs and the electrical resistance change due to shear deformation of the epoxy matrix between CNTs. Two different contact types (head to head and overlap) and three different deformation connections (Type-I, Type-II, and Type-III) are considered to model the electrical network. Using the constitutive relations, the model relates the matrix deformation between the CNTs to the macroscale deformation of the composite. To validate the modeling results, experiments are performed using a four circumferential ring probe method. A parametric study is performed to investigate the effect of the total number of initial contact types, ratio of contact types, and number of potential Type-II deformation connections on electrical response. The theoretical predictions are validated with experiments for the first two stages of deformation and an optimal combination of deformation connections are obtained to have a close match with experimental findings.

Experiments are performed to understand the electro-bending behavior of conductive jute/epoxy curved composites for monitoring of damage under four-point bending. A well-connected electrical network in the laminated curved composite is obtained by wet flocking micro carbon fibers between laminates and dispersing carbon nanotubes (CNTs) within the matrix. By embedding only 0.1 wt% of CNTs into the composites, the effects of carbon fiber length and density on electro-bending behavior is studied. The normalized curved beam strength (curved beam strength/thickness) of composites marginally increased for a case of carbon fiber length of 350 µm and fiber density of 500 fibers/mm2 compared to composites with no carbon fibers, however for all other cases, it showed slight decrease. The electro-bending behavior of composites of carbon fiber length of 150 µm showed higher percentage resistance change both at crack initiation point as well as at failure of specimen compared to those of carbon fiber length of 350 µm. The longer fiber (350 µm) composites provided rich conductive network and formed new connections to compensate the increase in resistance due to damage growth.

A comprehensive experimental impact characterization study of novel impact energy absorbing (IEA) materials under impact shear loading is conducted. Electro-flocking process is employed to fabricate the novel fiber based padding materials, also known as flocked energy absorbing materials (FEAM). FEAM IEA panels are prepared by flocking 1–3 mm long, 6–60 denier nylon fibers onto a planar polyester fabric sheet. The impact energy absorption under combined pre-compression loading and shear impact loading is investigated using a custom built guided weight drop tower along with a specially designed pre-compression and shear loading fixture for this study. A parametric study is performed where the effect of fiber material properties such as flock fiber length , diameter and flock density (number of flock fibers per area) on IEA is investigated and they are later compared with that of Vinyl Nitrile (VN) foam materials . Padding material based on FEAM configurations showed remarkable improvement when compared directly to VN foam with a 135% increase in shear strain energy density for the high impact velocity loading condition. Additionally, for low velocity impact conditions, the FEAM based padding materials out performed with a 49% increase in shear strain energy density as compared to VN foam.

Early-stage damage detection could provide better reliability and performance and a longer lifetime of materials while reducing maintenance time of a variety of structures and systems. We investigate the early-stage damage formation and damage evolution in advanced multi-functional laminated aerospace composites embedded with a very small amount of carbon nanotubes (CNTs) in the matrix material and short carbon fibers along the Z-direction to reinforce the interlaminar interfaces. The three-dimensional (3-D) conductive network formed by the CNTs and the flocked carbon fibers allows for sensitive in-situ damage detection in materials in addition to providing improved mechanical properties such as superior fracture toughness for damage tolerance. We optimize several parameters such as fiber length, diameter, and density to generate an effective 3-D electrical conductive network, and characterize the responses of these composites under mechanical loading to investigate damage formation and evolution, advancing science and technology towards superior damage-tolerant and zero-maintenance structural materials.

This study examines the effects of preform architecture, surface treatment, and z-directional micro-fiber reinforcement on the interlaminar fracture performance of jute/epoxy laminated composites. Laminated composites were fabricated using an optimized vacuum infusion process. Fracture characterization studies showed surface treatments increased fracture toughness as a result of improved interfacial adhesion. Unidirectional preforms were found to decrease fracture toughness as compared to plain weave preforms due to reduced inter-ply interaction. The addition of z-direction reinforcement increased the composites’ Mode-I fracture toughness by 80% and increased interlaminar shear strength (ILSS) at the cost of decreased tensile strength and modulus.

A detailed experimental study is conducted using multi-walled carbon nanotubes (MWCNTs) as a sensory network to understand damage initiation and growth within the process zone of epoxy particulate composites under opening mode fracture loading. Thermoset epoxy resin composites are toughened with three weight fractions of carboxyl-terminated butadiene acrylonitrile copolymer (CTBN) rubber (10 phr, 20 phr and 30 phr). Single-edge notch tension (SENT) geometry and far-field tensile loading conditions are used for this study. A modified four-point probe methodology coupled with a high-resolution data acquisition system is employed to capture the electrical response within the process zone of fracture test specimens. For each composite, the damage initiation and growth associated with linear and non-linear deformation is analyzed and discussed with respect to the change in crack tip opening displacement (CTOD). Although the electrical response did not differ qualitatively with the addition of both 10 phr and 20 phr rubber to epoxy, addition of 30 phr of rubber showed a significantly different response both qualitatively and quantitatively. This is the result of several mechanisms such as disentanglement and stretching of epoxy matrix molecules, micro-crack blunting, debonding of rubber particles, void growth and propagation.

Nano-characterization studies using atomic force microscopy (AFM) was conducted to study the effect of accelerated ultra violet (UV) and thermal degradation on mechanical properties of Nylon textile fibers. Nylon fibers were exposed to UV radiation for six different hours using Q-UV Panel Weatherometer. The exposed fibers were molded in an epoxy plug for nanaoindentation using AFM. Progressive nanoindentation from surface to the center of the fiber was used to investigate the effect of degradation on gradation of Young’s modulus across fiber cross-section. it was identified that UV degradation decreases the Young’s modulus from center to surface of the fibers up to 144 hours of exposure. Reduction of Young’s modules at surface was greater than the center implying more deterioration at the surface. To investigate thermal degradation effect on Nylon fibers, the fibers were exposed to 175oC for four weeks. initial experimentation indicates that the thermal exposure causes gradual reduction of Young’s modules. Wide angle x-ray spectroscopy (WAXS) and Fourier Transform infra Red Spectroscopy (FTIR) are used to correlate the fiber chemical and micro-structured changes to the variation of nano-mechanical properties.

Mixed-mode dynamic crack growth behavior along an arbitrarily smoothly varying path in functionally graded materials (FGMs) under transient thermo-mechanical loading is studied. An asymptotic analysis in conjunction with displacement potentials is used to develop transient thermo-mechanical stress fields around the propagating crack-tip. Asymptotic temperature field equations are derived for exponentially varying thermal properties, and later, these equations are used to derive transient thermo-mechanical stress fields for a curving crack in FGMs. The effect of the transient parameters (loading rate, crack-tip acceleration, and temperature change) and temperature gradient on the maximum principal stress and circumferential stress associated with the propagating crack-tip is discussed. Finally, using the minimum strain energy density criterion, the effect of temperature gradient, crack-tip speeds, and T-stress on crack growth directions is determined and discussed.

A series of dynamic compressive experiments were performed to experimentally investigate the electrical response of multi-wall carbon nanotube (CNT)-reinforced epoxy nanocomposites subjected to split Hopkinson pressure bar (SHPB) loading. Low-resistance CNT/epoxy specimens were fabricated using a combination of shear mixing and ultrasonication. Utilizing the CNT network within, the electrical resistance of the nanocomposite was monitored using a high-resolution four-point probe method during each compressive loading event. In addition, real-time deformation images were captured using high-speed photography. The percent change in resistance was correlated to both strain and real-time damage. The results were then compared to previous work conducted by the authors (quasi-static and drop weight impact) in order to elucidate the strain rate sensitivity on the electrical behavior of the material. Furthermore, the percent change in conductivity was determined using a Taylor expansion model to investigate the electrical response based on both dimensional change as well as resistivity change during mechanical loading within the elastic regime. Experimental findings indicate that the electrical resistance is a function of both the strain and deformation mechanisms induced by the loading. The bulk electrical resistance of the nanocomposites exhibited an overall decrease of 40–65% and 115–120% during quasi-static/drop weight and SHPB experiments, respectively.

An experimental investigation was conducted to study the effect of quasi-static and dynamic compressive loading on the electrical response of multi-wall carbon nanotube (MWCNT) reinforced epoxy nanocomposites. An in-situ polymerization process using both a shear mixer and an ultrasonic processor were employed to fabricate the nanocomposite material. The fabrication process parameters and the optimum weight fraction of MWCNTs for generating a well-dispersed percolation network were first determined. Absolute resistance values were measured with a high-resolution four-point probe method for both quasi-static and dynamic loading. In addition to measuring the percentage change in electrical resistance, real-time damage was captured using high-speed photography. The real-time damage was correlated to both load and percentage change in resistance profiles. The experimental findings indicate that the bulk electrical resistance of the nanocomposites under both quasi-static and dynamic loading conditions initially decreased between 40%–60% during compression and then increased as damage initiated and propagated.

Mixed-mode dynamic crack growth behavior in functionally graded materials (FGMs) under thermo-mechanical loading is studied. Asymptotic analysis in conjunction with displacement potentials has been used to develop thermo-mechanical stress fields for a mixed mode propagating crack in a FGM. The shear modulus, mass density, thermal conductivity and coefficient of thermal expansion of the FGM are assumed to vary exponentially along the gradation direction. First, asymptotic temperature fields are derived for an exponential variation of thermal conductivity and later these temperature fields are used in deriving stress fields. Using asymptotic thermo-mechanical stress fields the variation of maximum shear stress, circumferential stress and strain-energy density as a function of temperature around the crack tip are generated. Finally, utilizing the minimum strain-energy density criterion and the maximum circumferential stress criterion, the crack growth direction for various crack-tip speeds, non-homogeneity coefficients and temperature fields are determined.

The experimental efforts towards understanding the fracture behavior of continuously graded Functionally Graded Materials (FGMs) using full-field optical methods are reviewed. Both quasi-static and dynamic fracture investigations involving mode-I and -II conditions are presented. FGM configurations with crack planes perpendicular to, parallel to, and inclined to the direction of compositional gradation are discussed. Different strategies adopted by various investigators to develop polymer-based FGM systems for experimental mechanics studies are also described in this overview. Major theoretical developments that have predated and paralleled the experimental studies have been presented as well. Finally, the paper notes a few potential new directions where further contributions are possible.

Thermo-mechanical stress field equations are developed for a mixed-mode crack propagating at constant velocity in homogeneous and isotropic materials using an asymptotic approach along with displacement potentials. Asymptotic temperature field equations are first developed for steady state temperature conditions using insulated crack-face boundary conditions. These temperature field equations are later used to derive the first three terms of thermo-mechanical stress field equations for a steady state propagating mixed-mode crack. Using these thermo-mechanical stress fields, various components of the stresses are developed, and the effects of temperature on these stress components are discussed. Further, strain energy density and the circumferential stress criteria are employed to study the effect of temperature and the crack-tip velocity on crack growth direction.

Quasi-static mixed mode stress fields for a crack in orthotropic inhomogeneous medium are developed using asymptotic analysis coupled with Westergaard stress function approach. In the problem formulation, the elastic constants E11, E22, G12, ν12 are replaced by an effective stiffness \({E=\sqrt {E_{11} E_{22}}}\), a stiffness ratio \({\delta =\left({{E_{11}}\mathord{\left/ {\vphantom {{E_{11}} {E_{22}}}}\right. \kern-\nulldelimiterspace} {E_{22}}} \right)}\), an effective Poisson’s ratio \({\nu =\sqrt {\nu_{12}\nu _{21}} }\) and a shear parameter \({k=\left({E \mathord{\left/ {\vphantom {E {2G_{12}}}}\right. \kern-\nulldelimiterspace} {2G_{12}}}\right)-\nu }\). An assumption is made to vary the effective stiffness exponentially along one of the principal axes of orthotropy. The mode-mixity due to the crack orientation with respect to the property gradient is accommodated in the analysis through superposition of opening and shear modes. The expansion of stress fields consisting of the first four terms are derived to explicitly bring out the influence of nonhomogeneity on the structure of the mixed-mode stress field equations. Using the derived mixed-mode stress field equations, the isochromatic fringe contours are developed to understand the variation of stress field around the crack tip as a function of both orthotropic stiffness ratio and non-homogeneous coefficient.

In this paper, we report on an experimental study of the deflection/penetration behavior of dynamic mode-I cracks propagating at two different crack velocities (slower and faster) toward inclined weak interfaces of three dissimilar angles ( α ): 30°, 45° and 60°. A simple wedge-loading specimen configuration as proposed by Xu et al. [Xu LR, Huang YY, Rosakis AJ. Dynamic crack deflection and penetration at interface in homogenous materials: experimental studies and model predictions. J Mech Phys Solids 2003;51:461–86], made of brittle Homalite-100, is used. A modified Hopkinson bar setup is used to achieve well-controlled impact loading conditions. Dynamic photoelasticity in conjunction with high-speed photography is used to capture real-time isochromatics associated with deflected/penetrated cracks.

The conceptual simplicity and the ability of cohesive finite element models to describe complex fracture phenomena makes them often the approach of choice to study dynamic fracture. These models have proven to reproduce some experimental features, but to this point, no systematic study has validated their predictive ability; the difficulty in producing a sufficiently complete experimental record, and the intensive computational requirements needed to obtain converged simulations are possible causes. Here, we present a systematic integrated numerical–experimental approach to the verification and validation (V&V) of simulations of dynamic fracture along weak planes. We describe the intertwined computational and the experimental sides of the work, present the V&V results, and extract general conclusions about this kind of integrative approach.

Transient mixed-mode elastodynamic crack growth along arbitrary smoothly varying paths in functionally graded materials (FGMs) is considered. The property gradation in FGMs is considered by varying shear modulus and mass density exponentially along the gradation direction. Crack tip out of plane displacement fields and their gradients are developed for propagating curved cracks of arbitrary velocity using asymptotic approach. The mode-mixity due to the inclination of curved crack with respect to property gradient is accommodated in the analysis through superposition of the opening and shear modes. The expansion of the displacement fields and their gradients around the crack-tip are derived in powers of radial coordinates with the coefficients of expansion depending on the instantaneous value of the local curvature of the crack path, time derivatives of crack-tip speed, and time derivative of mode-I and mode-II stress intensity factors. The effect of the transient terms instantaneous local curvature, crack-tip speed, time derivatives of crack-tip speed, and time derivative of mode-I and mode-II stress intensity factors on the contours of constant out of plane displacement are also discussed.

The alignment and blend of extracellular matrix (ECM) proteins give a tissue its specific mechanical properties as well as its physiological function. Various tissue engineering methods have taken purified ECM proteins and aligned them into gels, sponges and threads. Although, each of these methods has created aligned ECM, they have had many limitations including loss of hierarchal collagen structure and poor mechanical performance. Here, we have developed a new method to control ECM synthesis using self-assembled cells. Cells were seeded into custom designed, scaffold-free, micro-molds with fixed obstacles that harnessed and directed cell-mediated stresses. Cells within the microtissue reacted to self-generated tension by aligning, elongating, and synthesizing an ECM whose organization was dictated by the strain field that was set by our micro-mold design. We have shown that through cell selection, we can create tissues with aligned collagen II or aligned elastin. We have also demonstrated that these self-assembled microtissues have mechanical properties in the range of natural tissues and that mold design can be used to further tailor these mechanical properties.

We here report on a detailed experimental study whose goal is to investigate spontaneous crack propagation in bonded and intact materials subjected to quasi-static far-field tensile loading. The cracks nucleate from a tiny circular hole and are triggered by an exploding wire. They subsequently propagate under the action of a constant far-field load. Dynamic photoelasticity in conjunction with high speed photography is used to capture the real-time photoelastic fringe patterns (isochromatics) associated with crack propagation. Dynamic stress intensity factors of propagating cracks are determined and the results are successfully compared with Broberg’s classical model of self-similar mode-I crack growth.

In this paper, we report on an experimental study of spontaneous, mixed-mode, crack propagation in weakly bonded similar and dissimilar materials. A unique experimental configuration is proposed to induce spontaneous crack growth events along the interfaces. The cracks nucleate from tiny circular holes and are triggered by an exploding wire. They subsequently propagate under the action of a constant, far-field load. Dynamic photoelasticity in conjunction with high speed photography is used to capture the real-time isochromatics associated with crack propagation. In the case of identical materials, crack propagation is anti-symmetric with respect to the crack nucleation point while strong asymmetry is observed for the case of dissimilar materials. In both cases, cracks propagate at constant velocity from the initiation point. The time histories of dynamic stress intensity factors and of energy release rates of the propagating cracks along the bonded similar materials are also reported.

Quasi-static stress fields for a crack inclined to the direction of property gradation in functionally graded materials (FGMs) are obtained through an asymptotic analysis coupled with Westergaard's stress function approach. The elastic modulus of the FGM is assumed to vary exponentially along the gradation direction. The mode mixity due to the inclination of the property gradient is accommodated in the analysis through superposition of opening and shear modes. The first four terms in the expansion of the stress field are derived to explicitly bring out the influence of nonhomogeneity on the structure of the stress field. Using these stress field contours of constant maximum shear stress, constant maximum principal stress, constant first stress invariant and constant out of plane displacement are generated, and the effect of inclination of the property gradation direction on these contours is discussed.

A simple procedure was established to fabricate polyurethane-cenosphere particulate composite materials. Composites having four different volume fractions of cenospheres (hollow ceramic microspheres) ranging from 10 to 40% in increments of 10% were prepared and their mechanical properties were evaluated. A predictive model to estimate the fracture toughness of the composite was developed. The dynamic constitutive behavior of the composite in compression was investigated using the split Hopkinson pressure bar (SHPB) technique in conjunction with high-speed photography. The results of the material characterization indicated that addition of cenospheres decreased the density of the composite. The quasi-static stiffness, both in tension and compression, and the quasi-static fracture toughness of the composite increased with addition of cenospheres. The high strain rate constitutive behavior of 100% polyurethane showed monotonic stiffening whereas the composite at higher cenosphere volume fractions (40%) exhibited a stiffening-softening-stiffening behavior. Scanning Electron Microscopy (SEM) studies were also carried out to determine the failure mechanisms of the composite.

A generalized elastic solution for an arbitrarily propagating crack in Functionally Gradient Materials (FGMs) is obtained through an asymptotic analysis. The shear modulus and mass density of the FGM are assumed to vary exponentially along the gradation direction. The mode mixity due to the inclination of property gradient is accommodated in the analysis through superposition of the opening and shear modes. Using this asymptotic solution, contours of constant out of plane displacement are generated. The effect of inclination of property gradation direction and the crack speed on these contours is discussed.

A well-controlled and minimal experimental scheme for dynamic fracture along weak planes is specifically designed for the validation of large-scale simulations using cohesive finite elements. The role of the experiments in the integrated approach is two-fold. On the one hand, careful measurements provide accurate boundary conditions and material parameters for a complete setup of the simulations without free parameters. On the other hand, quantitative performance metrics are provided by the experiments, which are compared a posteriori with the results of the simulations. A modified Hopkinson bar setup in association with notch-face loading is used to obtain controlled loading of the fracture specimens. An inverse problem of cohesive zone modeling is performed to obtain accurate mode-I cohesive zone laws from experimentally measured deformation fields. The speckle interferometry technique is employed to obtain the experimentally measured deformation field. Dynamic photoelasticity in conjunction with high-speed photography is used to capture experimental records of crack propagation. The comparison shows that both the experiments and the numerical simulations result in very similar crack initiation times and produce crack tip velocities which differ by less than 6%. The results also confirm that the detailed shape of the non-linear cohesive zone law has no significant influence on the numerical results.

The dynamic behavior of materials is a subject of everincreasing interest to the technical community owing to applications ranging from shock and blast to crash, impact and ballistics. Hence, it has relevance to government, industry and academia. The enhanced interest in dynamic behavior is evident from the increase in the number of papers in Experimental Mechanics on this topic, as well as expansion of the Dynamic Behavior sessions at the SEM annual conferences. Since inauguration of the SEM Dynamic Behavior Technical Division in 2005, presentations on this topic at the annual conference have increased from two sessions (~10 papers) in 2005 to two tracks (~150 papers) in 2009 and 2010. This level of interest prompted the EM editor to suggest a special issue to address current issues on the dynamic behavior of materials. This special issue of Experimental Mechanics includes nine papers addressing topics of immediate interest to this technical community. The papers were selected from the written papers submitted to the Dynamic Behavior track at the 2010 SEM Annual Conference on Experimental and Applied Mechanics, Indianapolis, IN, USA, June 7–10, 2010. The major subject areas are: 1) Advancements in high strain rate testing, 2) Dynamic response of various materials, 3) Dynamic failure and fracture, and 4) Modeling of dynamic events. Hopkinson/Kolsky bar techniques are the most commonly used method for characterizing the high strain rate response of materials. Current dynamic testing methods can be linked to the pioneering work of Hopkinson [1] and Kolsky [2] in applying stress wave experiments to evaluate dynamic material response, and to Lindholm and co-workers [3] in reducing this technique to practice. They [3] developed a methodology for deriving the stress–strain response of a material using transient pulse shapes acquired from strain gages on both bars. The strain rate range for traditional Kolsky bar systems ranges from 10 s to 10 s. Higher strain rates can be achieved by reducing the specimen size and the bar diameter [4]. Small (fewmm or sub-millimeter) diameter Kolsky bar systems have been developed which extend the strain rate range beyond 100,000 s. However, strain gage measurement of the longitudinal stress waves in the bars becomes impractical at the small scale. The paper by Casem, Grunschel and Schuster, in this special issue of Experimental Mechanics, demonstrates the feasibility of optical techniques for replacing traditional strain gage measurements in miniaturized systems. The dynamic tension or compression response of materials is readily obtained with traditional Kolsky bar systems. Pure shear data can also be obtained with a torsion bar. This is detailed in the paper by Hokka, et al. on the high strain rate torsion response of ultra-fine grained aluminum. Modifications to traditional Kolsky bar systems have expanded the types of high strain rate tests that can be conducted using these systems. For example, Anton and Subhash [5] used a modified bar system with a small diameter incident bar to measure dynamic Vickers hardness for brittle materials. Nie, Chen, et al. [6] conducted dynamic flexural strength tests on glass through implementation of a four-point bend configuration in the Hopkinson bar. Nie and Chen also devised a ring-on-ring technique for measuring the dynamic equibiaxial flexural strength of glass at temperatures up to K.A. Dannemann (*) Southwest Research Institute, San Antonio, TX, USA e-mail: kdannemann@swri.org