Concept Of Configurational Forces Research Articles

Configurational forces in a phase field model for the cyclic fatigue of heterogeneous materials

The phase field model - a powerful tool - has been well established to simulate the fatigue crack evolution behavior. However, it is still hard to understand how each energy component in the phase field model contributes to crack evolution since the phase field method is based on an energetic criterion. In this work, we borrow the concept of configurational forces and show a straightforward way to examine the energetic driving forces in the phase field fatigue model. Results show that different parts of the configurational forces provide different energetic contributions during crack propagation.

Rate of change of J‐integral in creep‐fatigue condition

AbstractThe operational conditions in next generation power plants and other high temperature applications such as turbine blades in jet engines demand the component to perform under extreme conditions where metallic materials show time dependent deformation under cyclic loading conditions. Under creep‐fatigue loading condition, the crack tip is exposed to both time dependent and independent plastic deformation. Conventional crack characterizing parameters such as (C ) has shown good correlation with dominant damage‐based crack velocity, (d /d ) . However, the true definition or prediction of crack driving forces under such scenario are vague due to limited theoretical validity of the conventional crack tip characterizing parameters, such as or C . In this work, the concept of configurational forces are applied for the first time to understand the creep‐fatigue crack growth behavior. The crack growth is simulated using node‐release technique and the configurational forces are calculated using post processing the finite element results for calculation of d /d .

Configurational Forces in a Phase Field Model for Fatigue

AbstractIn the last decades, the phase field method has drawn much attention for its application in fracture mechanics because it offers a simple unified framework for crack propagation. The core idea of phase field models for fracture is to introduce a continuous scalar field representing the discontinuous crack. Recently, a phase field model for fatigue has been proposed along this path. The fatigue failure differs from the other fracture scenarios since cracks only occur after a considerable number of load cycles. As fracturing happens, changes of the material microstructure are involved, which causes the evolution of the structural configuration. Thus, a new mathematical description not based on traditional spatial coordinates but the material manifold is desired, which will serve as an elegant analysis tool to understand the energetic forces for crack propagation. Configurational forces are a suitable choice for this purpose, as they describe the energetic driving forces associated with phenomena changing the material itself. In this work, we present a phase field model for fatigue. Furthermore, the phase field fatigue model is analyzed within the concept of configurational forces, which provides a straightforward way to understand the phase field simulations of fatigue fracture.

The jumping dielectric breakdown behavior induced by crack propagation in ferroelectric materials: A phase field study

Ferroelectric materials often experience fracture and dielectric breakdown under large mechanical and/or electrical loads. These two failure behaviors can affect each other and may lead to new phenomena. This study predicts a new type of jumping dielectric breakdown during crack propagation in ferroelectric materials using a phase field model involving multiple order parameters. The driving forces for the evolution of polarization, fracture, and dielectric breakdown were analysed based on the concept of configurational forces. The jumping dielectric breakdown was attributed to the competition between crack propagation and breakdown initiation at the moving crack tip. The breakdown pattern is related to the polarization domain structure and is significantly influenced by the applied electric field and crack boundary conditions. Furthermore, the jumping breakdown associated with possible mechanical degradation of the material can change the driving and resistance forces for crack propagation. This study introduces a novel dielectric breakdown behavior during crack propagation and provides new insights into the coupling failure of ferroelectric materials.

Elucidating the effect of cohesive zone length in fracture simulations of particulate composites

The influence of the cohesive zone length on the crack driving force is quantified and analyzed in a representative system of particles dispersed in a matrix of a composite material. For heterogeneous material systems, e.g. particulate composites, it is known that as a crack approaches the particles, the crack driving force may increase (shielding) or decrease (anti-shielding) depending on the relative stiffness of the particles. These results have been established in numerous studies using the classical linear elastic fracture mechanics approach (LEFM). The cohesive zone method (CZM) introduces a length scale parameter, referred to as the cohesive zone (or fracture process zone) length scale, into the formulation of fracture mechanics. It is generally established that fracture mechanics predictions using the CZM are similar to those obtained using LEFM in the limit case where the process zone is very small relative to a suitable characteristic dimension of the problem. However, the influence of the length scale parameter has not been clearly demonstrated for crack propagation in a heterogeneous material system, especially when the cohesive zone length is not negligible. By considering a simple crack-particle-matrix system, it is shown that, in addition to the elastic properties, the process zone length scale parameter exhibits a critical influence on the crack driving force. For this study, the concept of configurational forces is utilized and the eXtended Finite Element Method (XFEM) is employed as a tool to simulate crack propagation. Through numerical simulations, it is shown that (i) the magnitude of the driving force vector directly depends on the length scale parameter and (ii) the direction of the driving force is largely influenced by the presence of a cohesive zone. This, in turn, alters the crack trajectory in the particulate system if the criterion for the direction of crack propagation depends on the orientation of the driving force vector. Towards this end, two different criteria for direction of crack propagation, namely maximum principal stress and maximum energy dissipation, are compared in the presence of a cohesive zone and the results are reported. The study reveals the crucial influence of the inherent length scale associated with the cohesive zone method when applied to crack propagation in particulate composite systems and elucidates important differences when comparing predictions from distinct theories of fracture mechanics.

Influence of the material inhomogeneity effect on the crack growth behavior in fiber and particle reinforced composites

If a crack grows through a material with variations in Young’s modulus, a variation in the crack driving force occurs at a constant loading. Recent papers have shown that this material inhomogeneity effect has a great influence on the crack growth behavior and the fracture toughness of the materials. The purpose of this paper is to investigate the material inhomogeneity effect in fiber- or particle reinforced materials where the crack circumvents the particles and grows only through the homogeneous matrix material. A finite element study is performed under application of the configurational force concept. The particles cause a spatial variation of the crack driving force, quantified by the near-tip J-integral, Jtip. Characteristic parameters of the Jtip-variation are determined as a function of the composite geometry and the matrix and particle properties. The study is made for a regular arrangement of particles, but the results can be also applied for composites with arbitrary particle locations. Implications for the fracture toughness of the composite are worked out. The validity limits of the numerical results and the deduced analytical expressions are discussed.

Effect of material inhomogeneity under creep and plastic to creep transition of cracks

The driving force of a crack in a non-linear elastic material is described by the conventional J-integral, J (Rice 1968). For elastic−plastic materials, J does not describe the crack driving force. However, it describes the intensity of the crack tip field and can be, therefore, used to quantify the fracture toughness (Rice 1968). For the high-temperature behaviour of materials where creep deformation dominated, analogous parameter to J-integral were deduced, the C*-integral and a similar parameter, the Ct-integral (Landes and Begley 1976). C* has been proven to have a good correlation with the creep crack growth rate for many materials, mostly under extensive creep conditions. However, it does not describe the crack driving force.Based on the concept of configurational forces, a J -integral for elastic–plastic materials, Jep, was derived, which is able to quantify the true crack driving force in accordance with incremental theory of plasticity [4]. Hereby, the plastic strain is treated as an eigen-strain. Jep can be applied also in cases of non-proportional loading, e.g. for a growing crack (Simha et al. 2008) or for cyclic loading conditions (Ochensberger and Kolednik 2015). In this work, the concept of configurational force is applied to evaluate the crack driving force under small, medium and extensive creep conditions. Hereby, the creep strain is treated as a time dependent eigenstrain. A case study is performed where the path dependences of the elastic–plastic J-integral, Jep, and the conventional parameters Ct and C* are studied for materials which undergo elastic+creep deformation, with material inhomogeneity.It has been confirmed in the recent studies (Kolednik et al. 2014, Tiwari et al. 2020) that the material inhomogeneity term affects the crack depending on the nature of material inhomogeneity. This effect is unknown for creep deformation and the same has been studies on idealized fracture specimen under creep deformation using configurational forces and finite element method simulating real situations of dissimilar metals used at high temperatures in nuclear power plants and jet engines.

Analysis of the Bimaterial Interface Cracks Based on Configurational Forces

Abstract In this paper, an innovative interface fracture criterion is proposed based on the concept of configurational forces in material space. In this criterion, the crack-tip configurational forces as the driving force are introduced to describe the interface crack evolution under mixed-mode loading conditions. And it assumes that the interface crack propagates due to the competition of resultant configurational forces with interface fracture toughness. The analytical expression of the configurational forces is obtained by differentiating the elastic strain energy density and conservative integral for interface cracks. And the relation of interface crack-tip configurational forces with classical complex intensity factors is obtained through strict mathematical deduction. The interface crack-tip configurational forces are evaluated for a classic interface crack problem covering a wide range of bimaterial oscillation indexes. The configurational forces-based interface fracture criterion is validated through series interface fracture experiments. The proposed criterion may provide a novel framework for the analysis of interface fracture under complex loading conditions.

Numerical calculation of crack driving force using the configurational force concept for elastic–plastic rail cracks

Numerical calculation of crack driving force using the configurational force concept for elastic–plastic rail cracks

Configurational forces and J-integrals in cyclic metal plasticity

The configurational force concept is known to describe adequately the crack driving force in linear fracture mechanics. It is unclear however, if and how the crack driving force can be defined in the case of elastic-plastic material properties. In metal plasticity, many materials exhibit hardening effects when sufficiently large loads are applied. Von Mises yield function with isotropic and kinematic hardening is a common assumption in many models. Kinematic and isotropic hardening turn out to be very important whenever cyclic loading histories are applied. This holds equally regardless of whether the induced deformations are homogeneous or non-homogeneous. The aim of the present paper is to discuss the effect of non-linear isotropic and kinematic hardening on the response of the configurational forces and to provide suitable concepts for the thermodynamic description of elastic-plastic fracture problems. Further, the applicability of the shown concepts is discussed.

Nanoscale evolution of stress concentrations and crack morphology in multilayered CrN coating during indentation: Experiment and simulation

The layered architecture approach allows designing mechanical and fracture properties of hard coatings. The current study investigates the performance of a multilayered CrN coating, consisted of 5 μm CrN sublayers of very similar mechanical properties and microstructure but different residual stress states, during in-situ wedge indentation. A finite element model of the indentation was developed and validated against measurements of the local multiaxial stress fields during indentation, characterized by means of X-ray nanodiffraction analysis with a spatial resolution of 500 nm. By means of numerical fracture mechanics the effect of the multilayered structure on the formation and morphology of mode II cracks is analyzed. The configurational force concept was applied to investigate the crack driving forces and crack extension angles of static cracks in different geometrical arrangements. The simulation results agree well with the experimental findings and reveal a shielding effect preventing an interface-near crack from entering the CrN layer with the higher compressive residual stresses. Furthermore, the possibility to match the numerical results with the locally resolved experiments allowed determining validated material parameters for the deformation and fracture behavior. The work revealed e.g. that a KIIC of around 1 MPa∙m1/2 is an appropriate choice for the investigated CrN coating.

Application of the material inhomogeneity effect for the improvement of fracture toughness of a brittle polymer

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.

Driving forces on dislocations – An analytical and finite element study

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.

Development of Damage-Tolerant and Fracture-Resistant Materials by Utilizing the Material Inhomogeneity Effect

AbstractThe 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.

Configurational forces in cyclic metal plasticity

The configurational force concept is known to describe adequately the crack driving force in linear fracture mechanics. It seems to represent the crack driving force also for the case of elastic-plastic material properties. The latter has been recognized on the basis of thermodynamical considerations. In metal plasticity, real materials exhibit hardening effects when sufficiently large loads are applied. Von Mises yield function with isotropic and kinematic hardening is a common assumption in many models. Kinematic and isotropic hardening turn out to be very important whenever cyclic loading histories are applied. This holds equally regardless of whether the induced deformations are homogeneous or non-homogeneous. The aim of the present paper is to discuss the effect of nonlinear isotropic and kinematic hardening on the response of the configurational forces and related parameters in elastic-plastic fracture problems.

Analysis of crack growth under rolling-sliding contact

The work focuses on the calculation of shear crack growth with crack driving forces regarding cyclic elastic-plastic material behaviour. The load influence is described by the maximum contact pressure, and slip. The contact pressure and slip distribution in the contact patch are calculated using a 2D finite element model representing a wheel-rail contact. The configurational force concept is used to determine the crack driving forces in a cyclically plastified rail material during the wheel passage. The dependence of the crack driving force and the crack path on the loading conditions is shown. The results are qualitatively compared to experiments.

Crack arrest in thin metallic film stacks due to material- and residual stress inhomogeneities

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.

Material forces: An insight into configurational mechanics

The concept of material or configurational forces, albeit not new, is one of those innovations in theoretical mechanics that has struggled to reach the success of wide-spread acceptance, or even familiarity. Perhaps, one reason for this is to be found in the few available introductory examples or in the non-trivial physical-mathematical approach often taken to establish this concept, although by no means more complex than other treatments in non-linear continuum mechanics. With this work we aim at contributing to the dissemination of configurational mechanics concepts by guiding the reader through an introductory analytical example step by step and comparing it to numerically obtained results. The numerical model is solved with OpenGeoSys (OGS-6), an open-source, C++-based, object-oriented finite element platform for the thermo-hydro-mechanical analysis of coupled processes in fractured porous media. In the spirit of the open-source philosophy, and to enable the readers to reproduce the example themselves, both the source code and the input files are available online. The example highlights—in a simple and intuitive manner—several insightful aspects related to configurational mechanics.

Crack driving force in twisted plywood structures.

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.

Material configurational forces applied to mixed mode crack propagation

The concept of material configurational forces is applied to predict the mixed mode crack propagation. A new fracture criterion based on the resultant of configurational forces (termed as C-force criterion) is proposed. The basic assumption is that the onset of crack growth occurs when the resultant of configurational forces reaches a critical value and the crack growth takes place in the direction of resultant configurational forces. An implementation of the configurational forces into the finite element is presented. The newly proposed C-force criterion is further validated through a series of examples. It is concluded that the predictions of mixed-mode crack propagation by C-force criterion are in good agreement with experimental data in the open literatures. In addition, an experimental procedure on evaluation the configurational forces is proposed by using the digital image correlation. It is demonstrated that the C-force criterion provides a more convenient and accurate procedure to predict the mixed mode crack propagation.