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The evolution of essentially periodic crack patterns appears in many natural and technical processes. For example, typical cases of periodic crack patterns are known from drying soils, from the formation of basalt columns, from high temperature loaded ceramics, from fissure formation in coke, and from drying protein solution drops. The appearance of more or less periodic crack patterns is the result of cascades of bifurcation-instabilities of the propagation process. There exist established, mathematically rigorous criteria for the bifurcation of the crack growth process of two initially equally long parallel cracks (Nemat-Nasser et al., 1978; Bazant et al., 1979). These criteria require the determination of the mutual influence of the neighboring cracks on their growth by calculation of partial derivatives. If discretization methods are used for simulating such a growth process, the calculation of these partial derivatives may become very sensitive with respect to the density of the spatial discretization. This is especially true if strong gradients of a crack driving eigenstress field appear as, for instance, in chemical diffusion processes. In the present paper, an alternative approach is introduced, which circumvents estimations of partial derivatives and, in addition, provides a more realistic picture of the generation of crack patterns. This approach is inspired by a computationally efficient method for investigating the buckling and post-buckling behavior in structural mechanics by introducing small imperfections. As a typical example, in which the approach introduced here is especially beneficial, the simulation of self-organized crack pattern evolution in alkali feldspar, a very common brittle crystal, is presented. There, the cracks are driven by eigenstrains caused by cation exchange between the crystal and a salt melt. Comparisons between the character of the pattern formation in the simulation and in experiments show excellent agreement. Furthermore, by combining simulations and experiments the J c -value can be determined at considerably high accuracy. [ABSTRACT FROM AUTHOR]

Twisted plywood architectures can be observed in many biological materials with high fracture toughness, such as in arthropod cuticles or in lamellar bone. Main purpose of this paper is to analyze the influence of the progressive rotation of the fiber direction on the spatial variation of the crack driving force and, thus, on the fracture toughness of plywood-like structures. The theory of fiber composites is used to describe the stiffness matrix of a twisted plywood structure in a specimen-fixed coordinate system. The driving force acting on a crack propagating orthogonally to the fiber-rotation plane is studied by methods of computational mechanics, coupled with the concept of configurational forces. The analysis unfolds a spatial variation of the crack driving force with minima that are beneficial for the fracture toughness of the material. It is shown that the estimation of the crack driving force can be simplified by replacing the complicated anisotropic twisted plywood structure by an isotropic material with appropriate periodic variations of Young’s modulus, which can be constructed based either on the local stiffness or local strain energy density variations. As practical example, the concepts are discussed for a specimen with a stiffness anisotropy similar to lamellar bone. Statement of Significance Twisted plywood-like structures exist in many natural fiber composites, such as bone or insect carapaces, and are known to be very fracture resistant. The crack driving force in such materials is analyzed quantitatively for the first time, using the concept of configurational forces. This tool, well established in the mechanics of materials, is introduced to the modeling of biological material systems with inhomogeneous and anisotropic material behavior. Based on this analysis, it is shown that the system can be approximated by an appropriately chosen inhomogeneous but isotropic material for the calculation of the crack driving force. The spatial variation of the crack driving force and, especially, its local minima are essential to describe the fracture properties of twisted plywood structures. [ABSTRACT FROM AUTHOR]

Abstract: A material with spatial variation in the elastic modulus E can have a much higher apparent fracture resistance and fracture stress than a comparable homogeneous material. The effect occurs due to the strong decrease of the crack driving force, which leads to crack arrest when the crack tip is located in the region with low elastic modulus. From the results of exemplary numerical studies and simple fracture mechanical considerations, models are derived in order to predict the fracture stress and fracture toughness of the inhomogeneous materials. It is shown that high values of fracture stress and fracture toughness can be reached if the amplitude of the E variation is high enough to provide crack arrest and the wavelength of the E variation is small. The beneficial effect of material property variations also occurs if the width of the compliant region is very thin and the loss in stiffness of the structure is almost negligible. The concept is applicable for various types of composite materials; examples are presented. [Copyright &y& Elsevier]

Highlights: [•] The compendia for SIF K II, K III and Keq were given for a/c and crack depths a/t. [•] The Keq /K III,0 ratio has values between 0.45 and 0.5 for c/a =2 at any crack depth. [•] Experiment confirms fatigue crack propagation under significant influence of Mode II. [Copyright &y& Elsevier]

Abstract: The concept of ΔJ cyclic has been extended to fatigue initiation emanating from notch. The parameter is then named ΔJρ . Validation of this parameter is made by fatigue tests made on Roman tile specimens made in X52 pipe steel. Here, fatigue initiation is detected by acoustic emission. It has been found that the fatigue initiation decreases after hydrogen absorption. This can be explained by interaction of hydrogen and plasticity as can be seen for tensile and fracture behaviour of X52 steel after introduction of hydrogen. [Copyright &y& Elsevier]

Abstract: The concept of configurational forces is applied to demonstrate the application of the concept of configurational forces in the numerical simulation of crack growth and fracture processes. It is shown, how material property variations at an interface affect the crack driving force and how the criterion of maximum dissipation is used to evaluate the direction of crack propagation. Fatigue crack growth experiments were conducted on diffusion welded bimaterial specimens consisting of a high-strength steel and soft ARMCO iron. Two cases are considered: (1) specimens with an interface perpendicular to the initial crack orientation, and (2) specimens with an inclined interface. The numerical simulation with the concept of configurational forces show that not only variations of the elastic modulus and/or the yield stress have a tremendous influence on the crack driving force, the crack growth rate, and the curvature of the crack path, but also the thermal residual stresses that resulted from a rather small difference of the coefficient of thermal expansion. [ABSTRACT FROM AUTHOR]

Abstract: The concept of configurational forces is applied to demonstrate the application of the concept of configurational forces in the numerical simulation of crack growth and fracture processes. It is shown, how material property variations at an interface affect the crack driving force and how the criterion of maximum dissipation is used to evaluate the direction of crack propagation. Fatigue crack growth experiments were conducted on diffusion welded bimaterial specimens consisting of a high-strength steel and soft ARMCO iron. Two cases are considered: (1) specimens with an interface perpendicular to the initial crack orientation, and (2) specimens with an inclined interface. The numerical simulation with the concept of configurational forces show that not only variations of the elastic modulus and/or the yield stress have a tremendous influence on the crack driving force, the crack growth rate, and the curvature of the crack path, but also the thermal residual stresses that resulted from a rather small difference of the coefficient of thermal expansion. [ABSTRACT FROM AUTHOR]

This paper presents a case study, examining the influence of a sharp bimaterial interface on the effective crack driving force in a fracture mechanics specimen. The inhomogeneity of the elastic modulus in linear elastic and non-hardening and hardening elastic–plastic bimaterials is considered. The interface is perpendicular to the crack plane. The material properties and the distance between the crack tip and the interface are systematically varied. The effect of the material inhomogeneity is captured in form of a quantity called “material inhomogeneity term”, Cinh. This term can be evaluated either by a simple post-processing procedure, following a conventional finite element stress analysis, or by computing the J-integral along a contour around the interface, Jint. The effective crack driving force, Jtip, can be determined as the sum of Cinh and the nominally applied far-field crack driving force, Jfar. The results show that Cinh can be accurately determined by both methods even in cases where Jtip-values are inaccurate. When a crack approaches a stiff/compliant interface, Cinh is positive and Jtip becomes larger than Jfar. A compliant/stiff transition leads to a negative Cinh, and Jtip becomes smaller than Jfar. The material inhomogeneity term, Cinh, can have the same order of magnitude as Jfar. Based on the numerical results, the dependencies of Cinh on the material parameters and the geometry are derived. Simple expressions are obtained to estimate Cinh. [Copyright &y& Elsevier]

The current paper discusses concepts for implementing distinct edge dislocations into continua. Such dislocation models are successful, if they correctly predict both the stress- and displacement field around the dislocation line and the driving force on the dislocation in the presence of an external stress state. In addition, it is desired to realize the dislocation model by finite element programs. It is shown that the dislocation models available in literature do not fulfill these conditions, since they do not yield the correct driving force terms. Additional defect structures are investigated in order to work out a more successful dislocation model. Several methods are applied to derive the driving force on the dislocation for each model, (i) the configurational force concept, (ii) a thermodynamic concept based on the interaction energy, (iii) a relationship based on conservation integrals and the dislocation density. The results are compared to the classical Peach-Koehler solution. Two different procedures are worked out to correctly model a single edge dislocation, a numerically very simple method in form of two strips with prescribed eigenstrain components, which are considered consecutively, and a numerically more sophisticated concept, denominated as "cut-displace-glue" procedure. [ABSTRACT FROM AUTHOR]

This paper presents a method to determine the optimal static compress normal stress level for alternate torsional loaded tabular bar in order to ensure longer lifetime. Numbers of cycles to failure of the springs, which have been subjected to static compress normal stress on different levels were obtained experimentally. The paper analysed the stress state for biaxial loaded tabular torsion springs for different theoretical criterions as Columg-Mohr, Drucker-Prager criterion, the Sines criterion, criterion Crossland and Dang Van fatigue criterion. The analysis results are compared with the experimentally obtained average values. Comparison between the experimentally obtained and calculated theoretical points of the stress state, indicating that the longest life expectancy reached the point closest to the area of the double-axle stress state endurance in all measures except the Drucker-Prager criterion. Also theoretical results, from mentioned criteria, show that with increasing constant compression stress at a constant alternating torsional stress, the points are shifted from the area of safe to the area of fatigue failure. [ABSTRACT FROM AUTHOR]

Retardation of fatigue crack growth rate due to the introduction of thin, compliant and/or soft interlayers is investigated. The mechanism is the reduction of the crack driving force in the interlayer. Fatigue tests are conducted on composites made of high-strength aluminum alloy as matrix and technically pure aluminum or adhesive as interlayer material. The adhesive interlayer causes an increase in fatigue life by a factor 20 or more, whereas the aluminum interlayer yields only a moderate improvement. Numerical simulations based on the configurational force concept are utilized for understanding. The results show new possibilities for the design of fatigue-resistant materials. [ABSTRACT FROM AUTHOR]

The recently developed European flaw assessment procedure SINTAP was applied to the failure analysis of a broken fork of a forklift. Based on the service load at failure critical crack sizes were determined at different analysis levels of the procedure. It was shown in the present case study that the reason of the failure was defective design. [Copyright &y& Elsevier]

Abstract: The standards for characterization of fracture toughness of metals are focused on the calculation of fracture parameters based only on in-plane displacements of the specimen tested. Although fracture is a three-dimensional problem, out-of-plane displacements of the specimen tested are not mentioned in those documents. Since three-dimensional displacement measurement is available, it is worth investigating its potential uses in fracture tests. In this work, the fracture toughness of a structural steel was assessed through standard tests, measuring three-dimensional surface displacements. An alternative Crack Tip Opening Displacement calculation was introduced. The fracture initiation was inferred from the out-of-plane displacements, finding good agreement with results from R-curves. [Copyright &y& Elsevier]