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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.

Iron−silicon steels have excellent magnetic and electrical properties, especially, with increased silicon and aluminum contents. However, increasing alloying with Si and Al reduces the workability of the material, and spontaneous cleavage fracture may occur during production. The main influence factors on the occurrence of cleavage fracture of Fe−Si−Al alloys are investigated in this paper. Fracture mechanics tests are performed at various temperatures and loading rates. The effects of specimen orientation and strain aging are studied. The tests result surprisingly high fracture toughness values. However, cleavage fracture regions are found in the pre-fatigue regions of the specimens, i.e. at much lower loads. In order to resolve this effect, the strain rates during the various fatigue- and fracture experiments are estimated by an analytical model. Additional fatigue experiments are performed at various frequencies where the stress intensity range is increased until cleavage fracture is detected. Similar experiments are conducted at increasing temperatures. The analyses reveal a significant transition behavior of the stress intensity at the onset of cleavage fracture, where the effects of decreasing temperatures and increasing strain rates are equivalent. Measures for avoiding cleavage fracture can be deduced from the results of this investigation.

Talcum reinforced polypropylene was enhanced with a soft type of polypropylene in order to increase the impact strength and damage tolerance of the material. The soft phase was incorporated in the form of continuous interlayers, where the numbers of layers ranged from 64 to 2048. A blend with the same material composition (based on wt% of the used materials) and the pure matrix material were investigated for comparison. A plateau in impact strength was reached by layered architectures, where the matrix layer thickness was as small or smaller than the largest talcum particles. The most promising layered architecture, namely, 512 layers, was subsequently investigated more thoroughly using instrumented Charpy experiments and tensile testing. In these tests, normalised parameters for stiffness and strength were obtained in addition to the impact strength. The multilayered material showed remarkable impact strength, fracture energy and damage tolerance. However, stiffness and strength were reduced due to the addition of the soft phase. It could be shown that specimens under bending loads are very compliant due to a stress-decoupling effect between layers that specifically reduces bending stiffness. This drawback could be avoided under tensile loading, while the increase in toughness remained high.

Miniaturized materials, in general, exhibit higher strength compared to their bulk counterparts. As a consequence, their resistance to fracture is often compromised. However, the effect of material inhomogeneities can be used to significantly improve the fracture toughness of thin film components. In this work, the material inhomogeneity effect on the crack driving force, caused by material property and residual stress variations in thin tungsten and copper stacks, is numerically investigated. To this purpose, a finite element analysis is performed using the concept of configurational forces. In this way, we are able to distinguish between the various inhomogeneity effects and draw conclusions about the effective crack driving force. It is demonstrated that the material inhomogeneity effect is not solely determined by the material property variations at the interfaces, since an important contribution emerges due to a smooth residual stress gradient within the layers. The possibility to separate the different effects represents an opportunity for cost efficient design of future reliable thin film microelectronic components.

The formability of newly developed steel grades is a key parameter for their successful implementation in the car body. In the present work, the influence of the microstructure on formability during air bending is studied. First- and third-generation advanced high strength steels with tensile strengths above 1000 MPa are investigated, which exhibit a broad range of microstructural constituents (ferritic bainite, bainite, martensite, and retained austenite). Interrupted bending experiments are performed on two grades of dual phase and complex phase steels, respectively, in order to reveal the microscopic deformation and failure processes. The formability in hole expansion tests is determined and used as a measure for the resistance of the materials against crack formation. The macroscopic deformation behavior of the materials is taken into account by measuring the differential strain hardening exponent and performing finite element simulations of the air bending process. Advantages and disadvantages of various microstructural features are worked out, and it is explained why the first-generation dual phase steel exhibits the lowest and the third-generation complex phase steel the best formability during air bending.

Measuring the local behaviour of a propagating crack in a quantitative manner has always been a challenge in the field of fracture mechanics. In-situ microcantilever testing inside a scanning electron microscope (SEM) is one of the most promising techniques for the investigation thereof. However, quantifying such experiments is fairly challenging. Here, for the first time we utilize a continuous measurement of the dynamic compliance in-situ to permit evaluation of the crack length. Microcantilever experiments have been performed on brittle single crystalline Si and nanocrystalline Fe to assess the stability of the setup, the applicability of the technique inside an SEM and to establish a correlation between stiffness and crack length. Subsequently, micromechanical fracture tests were performed on single crystalline, 〈001〉{001} oriented tungsten as a model material and continuous J-Δa curves were measured. The gathered data was evaluated with close relation to standardized fracture mechanics testing and showed an overall agreement with literature data. This novel possibility to measure J-Δa curve behaviour continuously and locally while also following the crack extension through in-situ imaging inside an SEM is generally applicable and will allow new insights in the crack propagation of modern materials. Keywords: In-situ microcantilever testing, Elastic-plastic fracture mechanics, Dynamic compliance measurement, Tungsten

Bilayered materials with different properties play an important role in several fields of engineering to improve the mechanical, thermal, electrical, magnetic characteristics of structures. In order to determine the fracture toughness of such bimaterials, experimental measurements must be combined with numerical calculations, which is a tremendous effort. Therefore, a procedure is presented which enables a simple determination of the (critical) stress intensity factor for bimaterial bend specimens. The procedure is applicable for nano- to macroscale cantilevers and three-point bend specimens consisting of linear-elastic or elastic-plastic film and substrate materials. By finite element computations, the procedure is verified for a wide range of Young's moduli combinations, layer heights, and crack lengths. Possible limitations of the procedure are worked out. Practical applications for concrete bimaterial systems are presented, as well as the usage as a failure assessment tool.

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.

The introduction of thin interlayers with low yield stress can greatly improve the strength and the fracture toughness of inherently brittle materials. The reason is that the spatial yield stress variation affects the crack driving force, which strongly decreases when the crack tip is located in the interlayer region, near the boundary to the hard matrix material. This can lead to crack arrest. The material inhomogeneity effect appears without previous delamination of the interlayer. The decisive parameters influencing the effect are the interlayer spacing (the wavelength of the yield stress variation), the interlayer thickness and the yield stress ratio between interlayer and matrix. Based on numerical simulations with the configurational forces concept, it is demonstrated how the architectural parameters of the multilayer must be chosen in order to enhance the fracture stress and the fracture toughness of the material. An iterative procedure is proposed to find the optimum configuration. It is found that the optimum wavelength is inversely proportional to the square of the applied stress. A similar relation is given for composites with spatial variations in Young's modulus.

The improvement of fracture strength by insertion of thin, soft interlayers is a strategy observed in biological materials such as deep-see sponges. The basic mechanism is a reduction of the crack driving force due to the spatial variation of yield strength and/or Young's modulus. The application of this “material inhomogeneity effect” is demonstrated in this paper. The effectiveness of various interlayer configurations is investigated by numerical simulations under application of the configurational force concept. Laminated composites, made of high-strength tool steels as matrix materials and low-strength deep-drawing steel as interlayer material, were manufactured by hot press bonding. The number of interlayers and the interlayer thickness were varied. Fracture mechanics experiments show crack arrest in the first interlayer and significant improvements in fracture toughness, even without the occurrence of other toughening mechanisms, such as interface delamination. The application of the material inhomogeneity effect for different types of matrix materials is discussed.

Lamellar bone is known to be the most typical structure of cortical bone in large mammals including humans. This type of tissue provides a good combination of strength and fracture toughness. As has been shown by John D Currey and other researchers, large deformations are associated with the appearance of microdamage that optically whitens the tissue, a process that has been identified as a contribution to bone toughness. Using finite-element modelling, we study crack propagation in a material with periodic variation of mechanical parameters, such as elastic modulus and strength, chosen to represent lamellar bone. We show that a multitude of microcracks appears in the region ahead of the initial crack tip, thus dissipating energy even without a progression of the initial crack tip. Strength and toughness are shown to be both larger for the (notched) lamellar material than for a homogeneous material with the same average properties and the same initial notch. The length of the microcracks typically corresponds to the width of a lamella, that is, to several microns. This simultaneous improvement of strength and toughness may explain the ubiquity of lamellar plywood structures not just in bone but also in plants and in chitin-based cuticles of insects and arthropods.

The evolution of the irradiation embrittlement of nuclear pressure vessel steels is determined experimentally using special specimen geometries. Such sub-sized w-shape eccentrically-loaded single edge cracked tension specimens are employed due to mounting and handling requirements. Stress intensity factor solutions are available in the literature for this geometry; however, they are inaccurate for smaller crack lengths. Therefore, new approximate solutions are presented in this work to determine the stress intensity factor for such a w-shape tension specimen for a wide range of crack lengths (0.05

In a multilayered structure with a crack, a spatial change in the mechanical properties of the material strongly influences the crack driving force. This material inhomogeneity effect can be utilized to improve the fracture toughness of a given structure by inserting thin, soft interlayers into the material. The effectiveness of this procedure has been demonstrated on high-strength materials, such as metallic alloys and ceramics. It is shown in this article that the material inhomogeneity effect can be also successfully applied to polymers and that it is possible to predict the improvement in fracture toughness by a numerical analysis. First, a numerical case study based on the configurational force concept is performed on a brittle polymer matrix with interlayers made of materials with different strength and Young’s modulus. After selecting the most appropriate interlayer material, a composite is fabricated, which contains a single interlayer. Fracture toughness experiments show approximately 7 times higher fracture toughness for the composite in comparison to the homogeneous matrix material. Numerical fracture mechanics tests are performed on homogeneous and composite material using the cohesive zone model for crack growth simulation. A procedure to calibrate the cohesive zone parameters is worked out, which is relatively easy for the homogeneous material, but more sophisticated for the composite material. The numerical analysis provides a tool for predicting the fracture toughness of multilayered polymer composites.

The effects of soft, polymeric interlayers on a brittle, mineral reinforced polymer matrix are investigated. Interlayers made of a standard polypropylene (PP) and a soft type of PP are introduced into matrix materials of either highly or moderately mineral particle reinforced PP. Single edge notch bending experiments are performed to characterize the fracture toughness of these composites. The experimental J-integral Jexp is used to describe the fracture toughness of the investigated materials. The multi-layered materials are compared to the homogeneous matrix material. A modified plotting technique is applied to more distinctly demonstrate the effects of soft layers on Jexp as a function of the crack extension Δa. The fracture toughness is evaluated and the slope of the J-Δa curves is used as a qualitative measure of crack growth resistance. In addition, the crack growth rate is recorded. The results show improvements in fracture toughness of almost twenty times of the matrix material, provided the material combination is chosen properly. This increase in fracture toughness is achieved due to a crack-arresting effect in the soft layers, which is followed by an energy-expensive crack re-initiation step.

The effect of local deformation on the fracture behaviour of TiAl alloys was investigated. Roller indentations impressed parallel to the crack plane significantly improve the fracture toughness. The residual strains present in the indentation zone were characterized by X-ray diffraction and modelled using finite element (FE) calculations. The experimentally observed macrostrains exhibit remarkable crystallographic anisotropies and are unequally shared between the major alloy constituents. The mechanisms behind the observed toughening have been discussed in terms of the residual strains and factors improving the crack tip plasticity. With regard to intended high-temperature applications, the temperature retention of the toughening effect was studied.

The current paper discusses the physically correct evaluation of the driving force for fatigue crack propagation in elastic–plastic materials using the $$J$$ -integral concept. This is important for low-cycle fatigue and for short fatigue cracks, where the conventional stress intensity range ( $$\Delta K$$ ) concept cannot be applied. Using the configurational force concept, Simha et al. (J Mech Phys Solids 56:2876–2895, 2008) , have derived the $$J$$ -integral for elastic–plastic materials with incremental theory of plasticity, $$J^{\mathrm{ep}}$$ , which is applicable for cyclic loading and/or for growing cracks, in contrast to the conventional $$J$$ -integral. The variation of this incremental plasticity $$J$$ -integral $$J^{\mathrm{ep}}$$ is studied in numerical investigations conducted on two-dimensional C(T)-specimens with long cracks under cyclic Mode I loading. The crack propagates by an increment after each load cycle. The maximum load is varied so that small- and large-scale yielding conditions prevail. Three different load ratios are considered, from pure tension to tension-compression loading. By theoretical considerations and comparisons with the variation of the crack tip opening displacement $$\delta _{\mathrm{t}}$$ , it is demonstrated that the cyclic, incremental plasticity $$J$$ -integral $$\Delta J_{\mathrm{actPZ}}^{\mathrm{ep}}$$ , which is computed for a contour around the active plastic zone of the growing crack, is physically appropriate to characterize the growth rate of fatigue cracks. The validity of the experimental cyclic $$J$$ -integral, $$\Delta J^{\mathrm{exp}}$$ , proposed by Dowling and Begley (ASTM STP 590:82–103, 1976), is also investigated. The results show that $$\Delta J^{\mathrm{exp}}$$ is correct for the first load cycle, however, not fully appropriate for a growing fatigue crack.

Fatigue crack propagation is by far the most important failure mechanism. Often cracks under low-cycle fatigue conditions and, especially, short fatigue cracks cannot be treated with the conventional stress intensity range $$\Delta K$$ -concept, since linear elastic fracture mechanics is not valid. For such cases, Dowling and Begley (ASTM STP 590:82–103, 1976) proposed to use the experimental cyclic $$J$$ -integral $$\Delta J^{\exp }$$ for the assessment of the fatigue crack growth rate. However, severe doubts exist concerning the application of $$\Delta J^{\exp }$$ . The reason is that, like the conventional $$J$$ -integral, $$\Delta J^{\exp }$$ presumes deformation theory of plasticity and, therefore, problems appear due to the strongly non-proportional loading conditions during cyclic loading. The theory of configurational forces enables the derivation of the $$J$$ -integral independent of the constitutive relations of the material. The $$J$$ -integral for incremental theory of plasticity, $$J^{\mathrm{ep}}$$ , has the physical meaning of a true driving force term and is potentially applicable for the description of cyclically loaded cracks, however, it is path dependent. The current paper aims to investigate the application of $$J^{\mathrm{ep}}$$ for the assessment of the crack driving force in cyclically loaded elastic–plastic materials. The properties of $$J^{\mathrm{ep}}$$ are worked out for a stationary crack in a compact tension specimen under cyclic Mode I loading and large-scale yielding conditions. Different load ratios, between pure tension- and tension–compression loading, are considered. The results provide a new basis for the application of the $$J$$ -integral concept for cyclic loading conditions in cases where linear elastic fracture mechanics is not applicable. It is shown that the application of the experimental cyclic $$J$$ -integral $$\Delta J^{\exp }$$ is physically appropriate, if certain conditions are observed.

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.

Steigende Anforderungen im Leichtbau machen den Einsatz des presshartenden Stahles 22MnB5 (PHS) immer wichtiger. Entscheidende Faktoren sind hohe Festigkeiten und gute Crashperformance. Das Crashverhalten wird industriell mit einem speziellen Dreipunkt-Biegeversuch charakterisiert. Um das Crashverhalten weiter verbessern zu konnen, wird in dieser Arbeit das Verhalten des PHS wahrend des Biegeversuchs untersucht und mit dem Verhalten hochfester Complexphasenstahle (CP1000 und CP1200) und Dualphasenstahle (DP1000) verglichen. Zusatzlich werden DP800 und DP1000 Proben verschiedenen Gluhbehandlungen unterzogen mit dem Ziel, unterschiedliche Gefuge und Verfestigungswerte einzustellen. Mittels unterbrochener Biegeversuche werden der Schadigungsverlauf und die Versagensmechanismen genau studiert. Diese Versuche zeigen, dass zwei unterschiedliche Versagensmechanismen auftreten, die von der Art des Gefuges des Stahles und der Hohe des Verfestigungsexponenten bestimmt werden.

It is well known that the application of the conventional $$J$$ -integral is connected with severe restrictions when it is applied for elastic–plastic materials. The first restriction is that the $$J$$ -integral can be used only, if the conditions of proportional loading are fulfilled, e.g. no unloading processes should occur in the material. The second restriction is that, even if this condition is fulfilled, the $$J$$ -integral does not describe the crack driving force, but only the intensity of the crack tip field. Using the configurational force concept, Simha et al. (J Mech Phys Solids 56:2876–2895, 2008), have derived a $$J$$ -integral, $$J^{\mathrm{ep}} $$ , which overcomes these restrictions: $$J^{\mathrm{ep}} $$ is able to quantify the crack driving force in elastic–plastic materials in accordance with incremental theory of plasticity and it can be applied also in cases of non-proportionality, e.g. for a growing crack. The current paper deals with the characteristic properties of this new $$J$$ -integral, $$J^{\mathrm{ep}}$$ , and works out the main differences to the conventional $$J$$ -integral. In order to do this, numerical studies are performed to calculate the distribution of the configurational forces in a cyclically loaded tensile specimen and in fracture mechanics specimens. For the latter case contained, uncontained, and general yielding conditions are considered. The path dependence of $$J^{\mathrm{ep}} $$ is determined for both a stationary and a growing crack. Much effort is spent in the investigation of the path dependence of $$J^{\mathrm{ep}} $$ very close to the crack tip. Several numerical parameters are varied in order to separate numerical and physical effects and to deduce the magnitudes of the crack driving force for stationary and growing cracks. Interpretation of the numerical results leads to a new, completed picture of the $$J$$ -integral in elastic–plastic materials where $$J^{\mathrm{ep}} $$ and the conventional $$J$$ -integral complement each other. This new view allows us also to shed new light on a long-term problem, which has been called the “paradox of elastic–plastic fracture mechanics”.

The so-called material inhomogeneity effect, which influences the crack driving force in inhomogeneous materials, has recently been found to contribute to the excellent behavior of some fracture resistant biomaterials. The current study aims to transfer these findings to engineering materials, by experimentally investigating the fracture behavior of multilayers consisting of a high-strength aluminum alloy and thin, soft polymer interlayers. Structures in crack divider and crack arrester (CA) configuration are tested. The results show that the structures in CA configuration exhibit a tremendously improved fracture resistance compared to the homogeneous bulk material. The reason is that cracks are completely arrested in the soft interlayers. This effect appears without delamination, i.e. it is basically different from the well-known delamination effect on weak interlayers.

We demonstrate in this paper that commercially available printing paper can reach very high fracture toughness, comparable to that of steel, simply due to a special arrangement of the paper sheets with respect to the crack. Fracture mechanics experiments are conducted on single sheets of paper as well as on multilayer specimens in crack divider and crack arrester configuration. It is demonstrated that an arrangement in crack arrester configuration leads to an increase of the fracture toughness by a factor ten. An explanation of the effect is given and the transferability to other materials is discussed.

A novel approach is introduced enabling characterization of the mechanical properties of hard coatings on the microscale. The method is based on bending experiments of chemically etched and focused ion beam shaped free-standing coating microcantilevers. The coating itself remains unaffected by the preparation, thus completely preserving its interface with surface features. The determination of fracture toughness, fracture stress and Young’s modulus is demonstrated on as-deposited and annealed sputtered CrN coatings, and reveals a dominant intergranular brittle fracture and annealing-induced grain boundary weakening.

Configurational forces invariably appear at the external boundaries of cracked bodies (including the crack faces), but it is unclear whether they influence crack growth. Also, it is unclear how such boundary configurational forces are related to the J-integrals calculated in the body. In this brief note, we (i) derive expressions for the surface configurational forces and determine their values on regions of the external boundaries with prescribed tractions or displacements, (ii) determine the relation between the far-field J-integral and the surface configurational forces, and (iii) show that surface configurational forces on the crack faces do not alter the relation between the near-tip and far-field J-integrals.

Summary: The cohesive zone model is used for the numerical simulation of crack growth in homogeneous specimens made of two different grades of polyethylene (PE) as well as in PE-bimaterials. The material data and the shapes of the cohesive function are deduced from experimental data by Ivankovic et al., Eng. Fract. Mech. 71, 2004, 657–668 and Ting et al., Polym. Eng. Sci. 46, 2006, 763–777. Fracture toughness parameters are evaluated from the simulated load versus displacement curves. The results show a significant influence of the arrangement of the two PE-grades in the bimaterial specimens, caused by both the different material properties and the different characteristic parameters of the cohesive function.

When a crack propagates in a heterogeneous elastic material, its crack driving force depends strongly on the distribution of the local stiffness near the crack tip. In materials with periodic spatial variations of the Young’s modulus, shielding and anti-shielding effects appear, i.e. the crack driving force is reduced or enhanced, compared to a homogeneous material. The effect is of great practical relevance, since it may lead to a strong increase of the fracture resistance. The concept of configurational forces (CCF) offers an established procedure for calculating the crack driving force. A very general relation for the periodic variation of Young’s modulus is applied, allowing the description of both harmonically varying and layered microstructures. Numerical results are presented. Two semi-analytical approximation concepts, based on either the CCF or the moduli perturbation concept, are introduced and discussed. Comparisons are provided and recommendations given.

Many biological materials, such as bone, nacre, or certain deep-sea glass sponges, have a hierarchical structure that makes them stiff, tough, and damage tolerant. Different structural features contributing to these exceptional properties have been identified, but a common motif of these materials, the periodic arrangement of structural components with strongly varying stiffness, has not gained sufficient attention. Here we show that the periodicity of the material properties is one of the dominant reasons for the high fracture resistance of these structures and their tolerance to short cracks. If the composite architecture fulfills certain design rules, which are derived in this paper, the stiff structure becomes fracture resistant and, most of all, flaw tolerant. This architectural criterion inspired from nature provides useful guidelines for the design of defect-tolerant resistant man-made materials.

The deformation behaviour of a dual-phase steel with a tensile strength of about 1 000 MPa is investigated at the micro level. In-plane strains are determined by means of in-situ tensile tests in the scanning electron microscope and automatic local deformation analysis (based on digital image correlation). Maps of strain at high and low magnification reveal the network-like formation of deformation bands. In detailed high resolution analyses the sites of highest strain (“hot spots”) are identified. Observations in metallographic cross-sections indicate that these hot spots are frequently the origin of damage initiation.

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.

Finite element computations are performed to analyze the phenomena of edge cracking and crack bifurcation in two ceramic laminates composed by tensile thick layers and compressive thin layers. The difference between these two laminates is the thickness of the compressive thin layers. Experimental results performed by one of the authors in previous works show that edge cracks exist in only one laminate, while crack bifurcation occurs in both laminates under bending. To understand the cracking phenomena observed in experiments, the energy release rates are calculated. Numerical results show that the initiation of crack bifurcation can be explained by the near-tip J-integral, provided that micro-cracks exist near the crack tip.

The fracture behavior of two metal matrix composites (MMCs) at different aging conditions is investigated both at the global and local levels. The study is focused on the processes of void initiation near the crack tip by either particle fracture or particle/matrix decohesion, and on fracture initiation. The global fracture properties are determined by conventional fracture mechanics tests. The local conditions for void and fracture initiation are determined using fractographic analyses and subsequent analytical computations, based on the HRR-field equations, mean-field theory, and a simple analytical model from literature. The correlation between the global and local fracture properties is studied. The applicability of existing models to predict the fracture toughness of MMCs is discussed. The results of the analyses suggest that the maximum principal stresses in the particles at the moment of void initiation are not constant, but exhibit a dependency on the composite yield strength.

This paper deals with the determination of the crack driving force in elastic-plastic materials and its correlation with the J-Integral approach. In a real elastic-plastic material, the conventional J-integral cannot describe the crack driving force. This problem has been solved in Simha et al. [1], where the configurational force approach was used to evaluate in a new way the J-integral under incremental plasticity conditions. The crack driving force in a homogeneous elastic-plastic material, Jtip, is given by the sum of the nominally applied far-field crack driving force, Jfar, and the plasticity influence term, Cp, which accounts for the shielding or anti-shielding effect of plasticity. In this study, the incremental plasticity J-integral and the crack driving force are considered for a stationary and a growing crack.

A two-dimensional finite element analysis is performed to model the behavior of fatigue cracks in bimaterial specimens made of diffusion-bonded ARMCO-iron and SAE 4340 steel with an interface perpendicular to the crack plane. The numerical analyses are based on experiments conducted by Pippan et al. [Mater. Sci. Eng. A 283 (2000) 225–233]. The concept of configurational forces is used to evaluate by post-processing the crack-tip shielding and anti-shielding effects that occur due to the differences in yield stress, hardening and coefficients of thermal expansion of ARMCO-iron and SAE 4340 steel. For given values of applied stress intensity range Δ K app and applied load ratio R app , the near-tip J -integral J tip is calculated at the maximum and minimum load. To allow for crack closure, the effective near-tip stress intensity range Δ K eff,tip is evaluated from the near-tip stress intensity range Δ K tip and the near-tip load ratio R tip . Calibration curves for homogeneous ARMCO-iron and SAE 4340 steel are used to calculate the crack growth rate da / dN from the values of Δ K eff,tip . The distance between interface and crack tip L is varied to simulate the behavior of a growing crack. The computed curves da / dN versus L curves are in good agreement with the experimental results.

The effect of thermal residual stresses in bimaterial structure with initial crack located near a sharp interface is discussed in this paper. Bimaterial compact tension (CT) specimen is used in the analysis, and the residual stresses are introduced by cooling of the specimen. The residual stresses affect the stress and strain fields near the crack tip, and the crack-driving force is different compared with that in the homogeneous material without residual stresses. This difference can be quantitatively expressed through an additional crack-driving force term—the material inhomogeneity term, Cinh. In this paper, it is evaluated using the post-processing procedure based on the concept of configurational forces, following a finite-element analysis. The results indicate that accurate numerical analysis of pre-cracked bimaterials should include the effect of thermally induced residual stresses. This effect cannot be neglected, even for bimaterials with homogeneous mechanical properties and inhomogeneity in thermal properties only (e.g. welded joints of ferritic and austenitic steel). Based on the obtained results, data from this study can be used in engineering practice to improve integrity and work safety of various inhomogeneous structures.

The paper deals with damage evolution near cyclically loaded edges of stamping or cutting tools. A specific cyclic edge-loading test procedure has been developed for characterising the behaviour of edges that are subjected to cyclic loading under high compressive mean stress. With this procedure, the local deformation behaviour and the damage evolution can be analysed after different load cycles. A cold work tool steel grade K340 Isodur produced by electroslag remelting technology was investigated.

This paper discusses the crack driving force in elastic–plastic materials, with particular emphasis on incremental plasticity. Using the configurational forces approach we identify a “plasticity influence term” that describes crack tip shielding or anti-shielding due to plastic deformation in the body. Standard constitutive models for finite strain as well as small strain incremental plasticity are used to obtain explicit expressions for the plasticity influence term in a two-dimensional setting. The total dissipation in the body is related to the near-tip and far-field J-integrals and the plasticity influence term. In the special case of deformation plasticity the plasticity influence term vanishes identically whereas for rigid plasticity and elastic-ideal plasticity the crack driving force vanishes. For steady state crack growth in incremental elastic–plastic materials, the plasticity influence term is equal to the negative of the plastic work per unit crack extension and the total dissipation in the body due to crack propagation and plastic deformation is determined by the far-field J-integral. For non-steady state crack growth, the plasticity influence term can be evaluated by post-processing after a conventional finite element stress analysis. Theory and computations are applied to a stationary crack in a C(T)-specimen to examine the effects of contained, uncontained and general yielding. A novel method is proposed for evaluating J-integrals under incremental plasticity conditions through the configurational body force. The incremental plasticity near-tip and far-field J-integrals are compared to conventional deformational plasticity and experimental J-integrals.

Micro-toughness in ductile fracture is defined as the plastic work dissipated per unit fracture surface area in the material separation processes of void growth and coalescence. A micromechanics model for the estimation of the size dependence of micro-toughness in ductile fracture is presented. Size effects are incorporated in the model using the conventional mechanism-based strain gradient plasticity (CMSG) theory. A finite element model of an axisymmetric representative unit cell with an initial spherical void is used to validate model predictions. Two characteristic length scales emerge from the model. The initial void radius sets the scale for the initial spherical void growth. For the subsequent void coalescence, the scale is set by the width of the intervoid ligament. Energy dissipation in ductile fracture is found to be dominated by the mechanisms of coalescence, and the micro-toughness in ductile fracture is found to be size dependent for dimple sizes approximately one order of magnitude larger than the material length scale.

Powder-metallurgy metal matrix composites (MMCs) with Al-6061 matrix and SiC-particles are analyzed by means of in situ tensile tests in the scanning electron microscope and automatic local deformation analyses. The particle size (10 and 100 μm) and the particle volume fraction (10% and 20%) are varied. For comparison the pure matrix material is also tested. The formation of the shear bands with increasing load is studied, and the differences in the shear band evolution in the different materials are worked out. Cracks are initiated by particle fracture and by matrix/particle decohesion. The crack tip opening displacements (COD) at the particle failure sites are determined, as well as the critical COD-values for particle cracks propagating into the matrix material. Qualitative relations between the global ductility of the MMCs and the deformation and damage behavior, both observed at the micro-scale, are worked out.

Das geschweiste Tankbodeneck eines vertikalen Lagertanks ist eine der gefahrdetsten Stellen des Tanks. Fullen und Entleeren oder Erdbeben fuhren durch das Abheben des Tankbodenecks zu hohen plastischen Dehnungen im Schweisnahtbereich des Tankbodenecks. Einbrandkerben am Ubergang von der Kehlnaht zum Grundmaterial verursachen Risse im Kerbgrund, die wachstumsfahig sind und die Undichtheit des Tanks zur Folge haben. Ein geo-metrisch und materiell nichtlineares Finite-Elemente-Modell fur zwei typische Tankgeometrien (hoher und breiter Tank) wird vorgestellt und mit der Ermittlung der Risstriebkraft (J-Integral) fur Risse im Grund von gegebenen Kerben kombiniert. Bei monotoner Belastung werden die berechneten J-Integrale mit experimentell ermittelten J-Integral-Rissverlangerungswerten verglichen und kritische Kerb- und Risstiefen festgestellt. Bei zyklischer Belastung wird ein Low-Cycle-Fatigue-Konzept fur einen wachstumsfahigen Riss im Kerbgrund vorgestellt. Zusatzlich wird ein Schadigungsindikator aktiviert. Die Ergebnisse werden zu einer Aussage uber die mogliche Undichtheit infolge intensiver plastischer Verformung in Verbindung mit Risswachstum zusammengefasst. Effect of monotonic and cyclic loading on the leaking of a shell to bottom attachment of a tank. The welded shell-to-bottom joint of a vertical liquid storage tank is one of the most endangered parts of a tank. Either filling as well as emptying or an earthquake excitation may lead to an uplift yielding high plastic strains near the welding seam of the shell to bottom attachment. Penetration notches near welding seams usually appear initiating a crack in the notch root. This crack may grow and cause leaking of the tank. A geometrically as well as materially non-linear finite element model for two relevant geometrical settings (tall tank and broad tank) is developed and combined with the crack driving force (J-integral) investigation for cracks in the root of notches with given depths. For monotonic loading the calculated J-integrals are compared with experimentally found J-integral-crack elongation values to find out the critical notch and/or crack depths. Due to cyclic loading the Low Cycle Fatigue concept for a growing crack in the notch root is applied. In addition, a damage indicator analysis is performed. These results are combined to find out whether the junction suffers leakage due to intensive plastic deformation combined with crack propagation.

Many biological materials, such as bone, nacre or biosilica, are known to be both stiff and tough. Their structure is hierarchical and appears to be optimized at all levels of hierarchy to combine the properties of its primary components, which are a tough protein and stiff mineral. Bone, for example, is a nanocomposite and the deformation pattern is clearly hierarchical. In lamellar cortical bone, fibrillar units aggregate into laminate sheets, in analogy to plywood. This lamellar structure has a dramatic effect on fracture toughness. Nacre and biosilica are also layered structures where thin organic layers separate sheets of aragonite mineral and biosilica, respectively. The high toughness of such layered biological structures is intriguing and may serve as a model for artificial layered composites. A possible origin for the toughness in layered structures is the deflection of racks at weak interfaces. However, we know from theoretical fracture mechanics that a variation of the material properties alone (even without inherently weak interfaces) may result in a shielding or anti-shielding effect to the crack tip, which leads to a change of the crack driving force and the energy consumed by the fracture process. In the current work, we therefore analyse the driving force onto cracks propagating inside a material where the Young’s modulus varies in a periodic way in a given direction (perpendicular to the lamellae). We derive a simple design criterion to obtain laminate structures without driving force for crack propagation perpendicular to the lamellae. We consider a crack in a plane configuration of unit thickness with the crack tip located at the point P, see Figure 1. Globally, the material is assumed to be elastic with a constant Young’s modulus Efar and a Poisson’s ratio m far away from the crack tip P. Inside a circular region with the radius R, however, the Young’s modulus E varies in space. We assume that this variation is periodic in x-direction with an average value E0. The specimen is loaded by a stress ∑ in y-direction on the upper and lower parts of the boundary Cfar (indicated as “o” and “u” in Fig. 1). The crack flanks are assumed to be stressfree. The stress field r near the crack tip T is described by the classical “near-tip field” expressed in polar coordinates r,h and the stress intensity factor KI, for details see the fracture mechanics literature, e.g., Gross et al., Ch. 4.2. The specific elastic strain energy density r e 2 can be calculated analytically for constant E and plane stress or strain conditions as

A material inhomogeneity in the direction of crack extension causes a difference between the near-tip crack driving force, Jtip, and the nominally applied far-field crack driving force, Jfar. This difference can be quantified by a material inhomogeneity term, Cinh, which is evaluated by a post-processing procedure to a conventional finite element stress analysis. The magnitude of the material inhomogeneity term is evaluated for cracks in an inhomogeneous welded joint made of a high-strength low-alloy steel. Both a crack proceeding from the under-matched (UM) to the over-matched (OM) and from the OM to the UM weld metal are treated. The effects of the inhomogeneity of the different material parameters (modulus of elasticity, yield strength, and strain hardening exponent) on Cinh and Jtip are systematically studied. The results demonstrate that the material inhomogeneity term is primarily influenced by the inhomogeneity of the yield strength. A crack growing towards an OM/UM interface experiences an accelerated crack growth rate or a pop-in, an UM/OM interface leads to a reduced crack growth rate or a crack arrest. The application of global assessment methods of the mismatch effect which are included in the Engineering Treatment Model (ETM) or in the Structural Integrity Assessment Procedures for European Industry (SINTAP) is discussed.

A new model for the estimation of the micro-toughness in ductile fracture is presented. Micro-toughness is defined as the plastic work dissipated per unit fracture surface area in the material separation processes of void growth and coalescence. Stereophotogrammetric measurements of the height and width of dimples on ductile fracture surfaces are used in conjunction with the model to determine the micro-toughness. A finite element model is used to validate the analytical model. With the new model the ratio between the micro-toughness as related to the fracture surface topology and the global fracture toughness (J-integral) values become physically reasonable. The model is applied to structural steels and a metal matrix composite. Implications to computational fracture mechanics models are discussed.

A procedure to predict the fracture toughness of a ceramic multilayer composite made of different phases is presented. The procedure requires experiments to measure the intrinsic fracture toughness of the phases and to determine the required material data. The numerical modeling includes a conventional finite element stress analysis and the calculation of the crack driving force based on the concept of configurational (material) forces. The procedure yields the fracture toughness of the composite as a function of the crack length. A bending bar consisting of layers made of alumina and an alumina–zirconia composite is investigated. The bar has a crack perpendicular to the interfaces. The spatial variations of both the thermal residual stresses and the elastic modulus induce shielding and anti-shielding effects on the crack, which are quantified. The numerically predicted fracture toughness is compared with the experimental values.