The energy jump condition for thermomechanical media in the presence of configurational forces

In the context of a propagating surface of discontinuity in a thermomechanical medium, this brief communication establishes a relationship between the supplies of material momentum, linear momentum, energy and entropy. The relationship is equivalent to the jump condition in energy and is also framed in the context of a driving traction.      

Failure theory via the concept of material configurational forces associated with the M-integral

A new failure theory based on the material configuration forces associated with the invariant M-integral is proposed to describe the content and evolution of the multi-defects localized in the body. The physical interpretation of the global M-integral is as the sum of the local energy release rate due to the self-similar expansion for each specific defect. It does provide an effective measure for the evaluation of damage level. It is found that the unique parameter of the M-integral cannot be used as a unified failure criterion to predict the damage evolution and the final failure due to the major obstacle that the critical value of the M-integral is not a problem-invariant constant and shows an apparent defect configuration-dependence. Consequently, a new failure parameter referred as the configurational damage parameter (abbreviated as Π-parameter) is proposed by the appropriate formulation via the M-integral, the remote uni-axial load, and the inner variable of the damaged area. A series of numerical examples are carried out to demonstrate that the critical value of Π-parameter is a material constant regardless of defect configurations. Furthermore, it is performed to validate the applicability of the Π-parameter as a failure criterion to predict the final failure of the locally damaged materials. Finally, a protocol of experimental measurement of the Π-parameter is proposed by method of digital image correlation to facilitate the wide application of the new failure criterion. It is concluded that the present failure theory via the configurational forces associated with the M-integral provides some outside variable features and has the advantage of predicting the structural integrity of damaged materials containing the locally distributed defects.     

Crack driving force and energy-momentum tensor in electroelastodynamic fracture

The energy flux integral and the energy-momentum tensor for studying the crack driving force in electroelastodynamic fracture are formulated within the framework of the nonlinear theory of coupled electric, thermal and mechanical fields based on fundamental principles of thermodynamics. This formulation lays a foundation for in-depth understanding of the fracture behavior of piezoelectric materials. Remarkably, the dynamic energy release rate thus obtained has an odd dependence on the electric displacement intensity factor for steady-state propagation of a conventional (unelectroded) crack with exact, electrically permeable, semi-permeable, or impermeable crack surface condition, which is in agreement with experimental evidence.     

A unified potential-based cohesive model of mixed-mode fracture

A generalized potential-based constitutive model for mixed-mode cohesive fracture is presented in conjunction with physical parameters such as fracture energy, cohesive strength and shape of cohesive interactions. It characterizes different fracture energies in each fracture mode, and can be applied to various material failure behavior (e.g. quasi-brittle). The unified potential leads to both intrinsic (with initial slope indicators to control elastic behavior) and extrinsic cohesive zone models. Path dependence of work-of-separation is investigated with respect to proportional and non-proportional paths—this investigation demonstrates consistency of the cohesive constitutive model. The potential-based model is verified by simulating a mixed-mode bending test. The actual potential is named PPR (Park-Paulino-Roesler), after the first initials of the authors’ last names.     

Softening behaviour and correction of the fracture energy

The area under the load–displacement softening curve gives the total external work on the test specimen and not the fracture energy. The fracture energy follows from half this area that is equal to the critical strain energy release rate at the first crack increment. For wood this is correctly applied for mode II. For mode I however, as for other materials, the total area is wrongly regarded, a factor 2 is too high. In some applications, based on crack increment cycles, the error is even a multiple of this factor 2. On the other hand, the measurements at softening may show an apparent decrease of the specific fracture energy that can be explained by a small crack joining mechanism when the ultimate state of the ligament of the test specimen is reached. Post fracture behaviour is thus not comparable with the behaviour of macro crack initiation.It is further shown, by the kinetics of the process, that the irreversible work of an ultimate loading cycle is proportional to the activation energy of the fracture process and not to the driving force of the process. This explains why the crack velocity decreases with the increase of this irreversible work and increases with the stress intensity increase.The fracture energy is a function of the Griffith strength and is thus related to the effective width of the test specimen and not to the ligament length. This also has to be corrected. Based on the derivation of the softening curve, the reported fracture toughness of 720 kN m^−1.5 of double-edge notched tests is corrected to 330 kN m^−1.5 and the value of 467 kN m^−1.5, based on the fracture energy, of the compact tension tests, is also corrected to the right value of 330 kN m^−1.5. A revision of published mode I data, based on the fracture energy obtained by the area of the softening curve, is thus necessary.     

Definition of a new predictor for multiaxial fatigue crack nucleation in rubber

From an engineering point of view, prediction of fatigue crack nucleation in automotive rubber parts is an essential prerequisite for the design of new components. We have derived a new predictor for fatigue crack nucleation in rubber. It is motivated by microscopic mechanisms induced by fatigue and developed in the framework of Configurational Mechanics. As the occurrence of macroscopic fatigue cracks is the consequence of the growth of pre-existing microscopic defects, the energy release rate of these flaws need to be quantified. It is shown that this microstructural evolution is governed by the smallest eigenvalue of the configurational (Eshelby) stress tensor. Indeed, this quantity appears to be a relevant multiaxial fatigue predictor under proportional loading conditions. Then, its generalization to non-proportional multiaxial fatigue problems is derived. Results show that the present predictor, which is related to the previously published predictors, is capable to unify multiaxial fatigue data.     

Prediction of mixed-mode fracture based on an elasto–plastic energy balance criterion

The maximum energy release rate criterion, i.e., G _max criterion, is commonly used for crack propagation analysis. This fracture criterion is based on the elastic macroscopic strength of materials. In the present investigation, however, the G _max criterion has been modified in order to accommodate the consideration of plastic strain energy. This modified criterion is extended to study the fatigue crack growth characteristics of mixed-mode cracks. To predict crack propagation due to fatigue loads, a new elasto–plastic energy model is presented. This new model includes the effects of material properties such as strain hardening exponent n, yield strength σ _y , and fracture toughness and stress intensity factor ranges. The results obtained are compared with those obtained using the commonly employed crack growth law and the experimental data.     

Peeling behavior of a viscoelastic thin-film on a rigid substrate

In order to study the adhesion mechanism of a viscoelastic thin-film on a substrate, peeling experiment of a viscoelastic polyvinylchloride (PVC) thin-film on a rigid substrate (glass) is carried out. The effects of peeling rate, peeling angle, film thickness, surface roughness and the interfacial adhesive on the peel-off force are considered. It is found that both the viscoelastic properties of the film and the interfacial adhesive contribute to the rate-dependent peel-off force. For a fixed peeling rate, the peel-off force decreases with the increasing peeling angle. Increasing film thickness or substrate roughness leads to an increase of the peel-off force. Viscoelastic energy release rate in the present experiment can be further predicted by adopting a recently published theoretical model. It is shown that the energy release rate increases with the increase of peeling rates or peeling angles. The results in the present paper should be helpful for understanding the adhesion mechanism of a viscoelastic thin-film.     

Influence of domain switching zones on the fracture toughness of ferroelectrics

The paper presents a fracture model for ferroelectric materials taking into account the hysteretic domain switching processes near to the tip of a macroscopic crack. The model is based on the balance of energy supplied by the driving forces, on the one hand, and the total of energies either dissipated by domain switching, stored in the crack wake region or consumed by the formation of new fracture surface, on the other hand. An internal variable theory describes the nonlinear coupled electromechanical material response within the framework of a three-dimensional continuum model. For simplicity, the complex orientation distribution function of domains in a polycrystalline ceramic is approximated by only six representative space orientations. The theory predicts certain dimensionless material parameter combinations which govern the change of fracture toughness under the application of different mechanical and electrical loadings. A comparison with data available in the literature for barium titanate ceramics yields a reasonable coincidence.     

The influence of model parameters and of the thermomechanical coupling on the behavior of shape memory devices

Shape memory materials (SMM) are receiving increasing attention for their use in applications that exploit their dynamic behavior. A thermomechanical model for devices with pseudoelastic behavior has been proposed in previous works [11] (Bernardini and Pence, 2005) [15] (Bernardini and Rega, 2005). The model takes into account several aspects of SMM behavior by means of seven model parameters.In this paper the effect of each parameter on the non-isothermal rate-dependent behavior of the device is studied, by paying particular attention to the effect of the thermomechanical coupling. Some overall synthetic indicators of the behavior of the shape memory device are defined in terms of the model parameters. By evaluating such indicators, a lot of information about the mechanical, thermal and thermomechanical effects on the device behavior can be gained before computing explicitly the response of the shape memory oscillator.The present work may provide a guide for the proper utilization of the model for the investigation of the dynamic response.     

Application of the material force concept to formation of discontinuities in soft sedimentary rocks

The possibility of rock joint formation from discontinuities which originate in poorly lithified sediments is presented. The mechanism for the development of these discontinuities along the maximum compressive stress T _max is discussed and quantitatively investigated. Micro-defects (holes, cavities) may exist in sediment due to non-ideal packing. It is shown that in certain situations, a physically warranted tendency to reduce the total energy of the system splits into two separate holes which move away relative to material particles (grains) along the T _max axis. The trace left by the moving hole is interpreted as a macro-discontinuity evolving with time into the closed mode I macro-crack. Some justifications for the mechanism are presented.     

Note on the Radial Deformation and Stresses in Anisotropic Nonhomogeneous Elastic Media

Abstract

In this paper we study the elasticity problem of a cylindrically anisotropic, elastic medium bounded by two axisymmetric cylindrical surfaces subjected to normal piessures (plane strain). The material of the structure is orthotropic with cylindrical anisotropy and, in addition, is continuously inhomogeneous with mechanical properties varying along the radius. General solutions in terms of Whittaker functions are presented. The results obtained by St. Venant for a homogeneous cylindrically anisotropic medium can be deduced from the general solutions. The problem of a solid cylinder of the same medium under the external pressure is also solved as a particular case of the above problem. Problems of the type covered in this paper are encountered in nuclear reactor design.     

Measurement of energy release rate and energy flux of rapidly bifurcating crack in Homalite 100 and Araldite B by high-speed holographic microscopy

High-speed holographic microscopy is applied to take three successive photographs of fast propagating cracks in Homalite 100 or in Araldite B at the moment of bifurcation. Crack speed at bifurcation is about 540 m/s on Homalite 100, and about 450 m/s on Araldite B. From the photographs, crack speeds immediately before and after bifurcation are obtained, and it is found that discontinuous change of crack speed does not exist at the moment of bifurcation in the case of Homalite 100, but exists in the case of Araldite B. From the photographs, crack opening displacement (COD) is also measured along the cracks as a function of distance r from the crack tips. The measurement results show that the CODs are proportional to √r before bifurcation. After bifurcation, the CODs of mother cracks are proportional to √r, though the CODs of branch cracks are not always proportional to √r. The energy release rate is obtained from the measured CODs, and it is found that energy release rate is continuous at bifurcation point in both cases of Homalite 100 and Araldite B. Energy flux that shows the energy flow toward a crack tip is also obtained.     

Transient thermal shock fracture analysis of functionally graded piezoelectric materials by the extended finite element method

Transient thermal dynamic analysis of stationary cracks in functionally graded piezoelectric materials (FGPMs) based on the extended finite element method (X-FEM) is presented. Both heating and cooling shocks are considered. The material properties are supposed to vary exponentially along specific direction while the crack-faces are assumed to be adiabatic and electrically impermeable. A dynamic X-FEM model is developed in which both Crank–Nicolson and Newmark time integration methods are used for calculating transient responses of thermal and electromechanical fields respectively. The generalized dynamic intensity factors for the thermal stresses and electrical displacements are extracted by using the interaction integral. The accuracy of the developed approach is verified numerically by comparing the calculated results with reference solutions. Numerical examples with mixed-mode crack problems are analyzed. The effects of the crack-length, poling direction, material gradation, etc. on the dynamic intensity factors are investigated. It shows that the transient dynamic crack behaviors under the cooling shock differ from those under the heating shock. The influence of the thermal shock loading on the dynamic intensity factors is significant.     

裂缝气液重力置换的流动实验及仿真

通过可视化模拟实验对真实裂缝下气液重力置换现象进行了模拟,得到了其气液界面现象与常规平板裂缝的差异;通过对压力、置换量等数据的处理证实了气液重力置换的机理;根据实验的液体漏失流量数据提出了钻井过程中漏失、置换、溢流区间;最后根据k-ε双方程模型进行了气液重力置换流动的仿真计算,得到三维裂缝流道中都是钻井液下部侵入,呈现一个近似的直角三角形形状。本文对现场钻井工程方案设计及安全钻井具有指导意义。     

Influence of Dislocation Pile-Up on Main Crack Propagation in Nanocrystals in the Hydrogen Environment

The influence of material micro-defects on the main crack growth under pure shear loading is studied theoretically.The mechanism behind the initiation of micro-cracks and crack propagation induced by dislocation accumulation near the grain boundary(GB)is mainly considered,and the influence of dislocation accumulation on the main crack propagation is analyzed.The research results reveal that the initiation of micro-cracks near the GB is prior to the propagation of the main crack.In a hydrogen environment,hydrogen can cause serious embrittlement of the crack tip and promote crack growth.The energy release rate in the main crack growth direction in the dislocation emission direction is the highest.Therefore,the main crack will eventually merge with the micro-cracks at the GB along the direction of the slip band,resulting in fracture of the crystal material.The research presented in this paper provides some new information for the first stage of crack propagation and contributes to the analysis of the mechanism of crystal metal fracture.     

Dynamic fracture mechanics analysis for composite material with material non-homogeneity in thickness direction

The problem considered here is the response of a non-homogeneous composite material containing some cracks subjected to dynamic loading. It is assumed that the composite material is orthotropic and all the material properties depend only on the coordinatey (along the thickness direction). In the analysis, the elastic region is divided into a number of plies of infinite length. The material properties are taken to be constants for each ply. By utilizing the Laplace transform and Fourier transform technique, the general solutions for plies are derived. The singular integral equations of the entire elastic region are obtained and solved by the virtual displacement principle. Attention is focused on the time-dependent full field solutions of stress intensity factor(SIF) and strain energy release rate. As a numerical illustration, the dynamic stress intensity factor of a substrate/functionally graded film structure with two cracks under suddenly applied forces on cracks face are presented for various material non-homogeneity parameters.     

J-integral and crack driving force in elastic–plastic materials

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.