The energy release rate for linear viscoelastic materials

For viscoelastic materials, the energy release rate is a fairly important parameter for determining whether the crack extends, but so far its meaning for viscoelastic materials is not yet clear enough. In this paper, the thermodynamic mechanical theory is used to derive the local and global energy release rate of viscoelastic materials when constitutive equations are given. Moreover, the method of deriving the viscoelastic energy release rate is discussed. The relation between the energy release rate and internal energy, Helmholz free energy is described. The equivalence between the local and global energy release rates is also proved after some doubts in previous papers are dispelled, although the upshot is not original. Furthermore, the concrete forms of the energy release rate for anisotropic, orthotropic and isotropic viscoelastic media are presented. The forms of the local and global energy release rates in the failure zone are discussed and the difference between the equation presented here and the one given in previous papers is pointed out.     

用能量图形面积法计算非线性弹性材料任意加载方式的能量释放率

从能量释放率G的定义出发,用图解法,即能量图形面积法,分别对线弹性材料和非线性弹性材料,以及在固定位移,或固定载荷,或任意加载方式的情况下,推导出能量释放率的计算公式.证明不同加载方式下的非线性弹性材料的能量释放率,在用能量图形面积法极限求导时,其数值是一样的.     

Strain energy density bounds for linear anisotropic elastic materials

Upper and lower bounds are presented for the magnitude of the strain energy density in linear anisotropic elastic materials. One set of bounds is given in terms of the magnitude of the stress field, another in terms of the magnitude of the strain field. Explicit algebraic formulas are given for the bounds in the case of cubic, transversely isotropic, hexagonal and tetragonal symmetry. In the case of orthotropic symmetry the explicit bounds depend upon the solution of a cubic equation, and in the case of the monoclinic and triclinic symmetries, on the solution of sixth order equations.     

Crack energy density and energy release rate for piezoelectric material

In this work, the concept of crack energy density (CED) was extended so as to be applied to piezoelectric material and its fundamental matters and properties were studied, and taking the knowledge about it into consideration, energy release rate for the material was newly derived. The definitions of CED, its mechanical and electrical contribution are given first and their path independent expressions are derived through the electromechanical energy conservation law. Subsequently, the loading path dependence of mechanical and electrical CEDs is discussed in detail. Some supplementary quantities related to CED and energy release rate are also defined and their path independent expressions are given. Energy release rate is derived through two opposite limit procedures, and the relations between energy release rate and other parameters are elicited through the discussions based on the fundamental properties of energy release rate.     

活性材料冲击释能行为研究进展

活性材料是一种具备释能特性的新型材料,其在冲击导致的高压/高温作用下可以发生化学反应,释放大量的化学能,因此在破片、聚能破甲战斗部等军事领域有广泛的应用潜力。为了实现对活性材料释能过程的设计与控制,推进活性材料武器化应用进程,就必须解答活性材料冲击释能行为中所包含的一系列复杂的力-热-化耦合问题。近40年来,对活性材料的冲击释能行为已开展了大量研究,本文在此基础上系统梳理了活性材料的冲击诱发化学反应机理、动力学以及相关效应的研究现状,重点关注活性材料的冲击释能实验表征技术、冲击诱发化学反应理论模型以及考虑力-热-化耦合的冲击压缩数值模拟方法等3方面的研究进展。总结认为,对活性材料冲击释能行为的研究已经具有一定的积淀,但目前对实验中超快化学反应行为的实时诊断研究还缺乏更加丰富、精细、直观的表征与探索,相关理论与数值模拟研究尚未建立能够完整描述活性材料冲击释能行为的力-热-化理论模型,缺乏能够从宏观尺度描述冲击释能行为的有效方法。因此,超快化学反应实验表征技术、宏观角度的力-热-化机理与模型建立及其数值模拟应用以及具备可调性能的活性材料制备新工艺3方面研究内容将是推进活性材料未来军事化应用的重点关注对象。     

On crack-tip strain energy release rate in non-principal directions of elasticity for simple layer plate of composite materials

In this paper,the fracture problem in non-principal directions of elasticity for a simple layer plate of linear-elastic orthotropic composite materials is studied.The formulae of transformation between characteristic roots,coefficients of elastic compliances in non-principal directions of elasticity and corresponding parameters in principal directions of elasticity are derived.Then,the computing formulae of strain energy release rate under skew-symmetric loading in terms of engineering parameters for principal directions of elasticity are obtained by substituting crack-tip stresses and displacements into the basic formula of the strain energy release rate.     

Strain energy release rate for interfacial cracks in hybrid beams

The finite element modeling and fracture mechanics concept were used to study the interfacial fracture of a FRP-concrete hybrid structure. The strain energy release rate of the interfacial crack was calculated by the virtual crack extension method. It is shown that the crack growth has three phases, namely, cracking initiation, stable crack growth and unstable crack propagation. The effects of geometric and physical parameters of the hybrid beam on the energy release rate were considered. These parameters include Young’s moduli of the FRP, the concrete and the adhesive, thickness of the FRP plate and adhesive, and the distance of FRP plate end from the beam end. The numerical results show that the energy release rate of the interfacial crack is influenced considerably by these parameters. The present investigation can contribute to the mechanism understanding and engineering design of the hybrid structures.     

Self-similar law of energy release before materials fracture

A general law of energy release is derived for stressed heterogeneous materials, being valid from the starting moment of loading till the moment of materials fracture. This law is obtained by employing the extrapolation technique of the self-similar approximation theory. Experiments are accomplished measuring the energy release for industrial composite samples. The derived analytical law is confronted with these experimental data as well as with the known experimental data for other materials.     

Anomalies associated with energy release parameters for cracks in piezoelectric materials

For a central crack in a piezoelectric plate, the mode-I stress intensity factor (K_I), electric displacement intensity factor (K_D), energy release rates (G, G_M) and energy density factor (S) are obtained from the finite element results. For the impermeable crack, the numerical results of K_I and K_D are coupled; this error is contrary to the uncoupled analytical solutions. The error has little effect on the total energy release rate G and energy density factor S, but in some cases, large errors in the mechanical energy release rate G_M are observed. G is global while SED is local. Also G is negative which defies physics where energy cannot be created while crack attempts to extend as implied by G. Computations should be made for the J-integral and also show that J becomes negative. What this shows is that the global fracture energy criterion is not suitable to address the local release of energy because it includes the overall energy which are irrelevant to fracture initiation being a local behavior. In addition, the case study shows that the energy density theory is the better fracture criterion for the piezoelectric material. According to the results of S, it retards the crack growth when the external electric field and piezoelectric poling are on opposite directions. This conclusion agrees with analytical and experimental evidence in the past references.     

On the calculation of energy release rate for viscoelastic cracked laminates

IntroductionGenerallyspeaking ,acrackinviscoelasticmaterialswillgrowinsomeunknownspeedeveniftheappliedloadisquasistatic,thusthemaindifficultyisinducedindervingtheenergyreleaserate .Knowledgeoftheconditiongoverningthedelaminationincompositelaminateswithviscoelasticlayersisofparamountimportanceinpracticalapplications.Forexample,inplasticencapsulatedICpackages,theinterfacialdelaminationbetweentheSilicondieandviscoelasticepoxymoldingcompoundunderthethermalloadingisthemainfailuremodeofthestructure…     

On consistent micromechanical estimation of macroscopic elastic energy,coherence energy and phase transformation strains for SMA materials

An apparatus of micromechanics is used to isolate the key ingredients entering macroscopic Gibbs free energy function of a shape memory alloy (SMA) material. A new self-equilibrated eigenstrains influence moduli (SEIM) method is developed for consistent estimation of effective (macroscopic) thermostatic properties of solid materials, which in microscale can be regarded as amalgams of n-phase linear thermoelastic component materials with eigenstrains. The SEIM satisfy the self-consistency conditions, following from elastic reciprocity (Betti) theorem. The method allowed expressing macroscopic coherency energy and elastic complementary energy terms present in the general form of macroscopic Gibbs free energy of SMA materials in the form of semilinear and semiquadratic functions of the phase composition. Consistent SEIM estimates of elastic complementary energy, coherency energy and phase transformation strains corresponding to classical Reuss and Voigt conjectures are explicitly specified. The Voigt explicit relations served as inspiration for working out an original engineering practice-oriented semiexperimental SEIM estimates. They are especially conveniently applicable for an isotropic aggregate (composite) composed of a mixture of n isotropic phases. Using experimental data for NiTi alloy and adopting conjecture that it can be treated as an isotropic aggregate of two isotropic phases, it is shown that the NiTi coherency energy and macroscopic phase strain are practically not influenced by the difference in values of austenite and martensite elastic constants. It is shown that existence of nonzero fluctuating part of phase microeigenstrains field is responsible for building up of so-called stored energy of coherency, which is accumulated in pure martensitic phase after full completion of phase transition. Experimental data for NiTi alloy show that the stored coherency energy cannot be neglected as it considerably influences the characteristic phase transition temperatures of SMA material.     

The Attainable Region of strain-invariant space for elastic materials

Within the theory of isothermal isotropic non-linear elasticity, the selection of the appropriate form for the strain energy function W in terms of the strain invariants is still an issue. The purpose of this paper is to introduce ideas and techniques which it is hoped will contribute to the task of finding an appropriate form for the strain energy. Three principal ideas are developed in this paper. Firstly, not all of invariant-space corresponds to real deformations. Constitutive equations only need to match real behaviour over a restricted part of invariant space, called the Attainable Region, bounded by states of deformation corresponding to uniaxial and equi-biaxial extension. Secondly, examples are given of how to exploit the fact that the Attainable Region is restricted. Mapping a deformation onto this region allows visualization of how close the deformation is to the well-understood uniaxial, equi-biaxial and simple shear deformations, and how this varies in space or time. Thirdly, acceptable strain invariants do not have to be obviously symmetric functions of the principal stretches. The ordered principal stretches are themselves invariants, and explicit unique algebraic expressions can be given through which the greatest, middle or least stretch can be calculated in terms of the usual invariants. Thus invariants can be chosen which are apparently non-symmetric functions of the ordered stretches.     

Comparison of energy release rate and minimum strain energy density for potential failure of composite with bi-material interface

An analytical method is developed to describe the fields of stress and displacement in a bi-material strip specimen with an edge interfacial crack. All of the basic governing equations, boundary conditions on crack surfaces and conditions of continuity along the interface are satisfied by the eigenfunction expansion method. The other boundary conditions are satisfied by the generalized variational principle. The stress intensity factors are calculated for determining the energy release rate and minimum strain energy density factor S_min that is used the strain energy density criterion. Problems with oscillatory singularity and contact zone are discussed. Not only the effects of bi-material modulus ratio, thickness ratio, Poisson's ratio and crack length to S_min, but also the influences of bi-material modulus ratio, thickness ratio to phase angle are presented. Among these parameters, particular situations where S_min become jeopardously high and lead to failure are discussed.     

Analysis of energy release rate for composite delaminated cylindrical shells subjected to axial compression

In this paper, the postbuckling governing equations and the analytical expression of the energy release rates associated with delamination growth in a compression-loaded cylindrical shell are derived by using the variational principle of moving boundary and the Griffith fracture criterion. The finite difference method is used to generate the postbuckling solutions of the delaminated cylindrical shells, and with these solutions, the values of the energy release rates are determined. In simulational examples, the effects of a wide range of parameters, such as delamination sizes and depths, boundary conditions, geometrical parameters, material properties and laminate stacking sequences on the energy release rates of axisymmetrical laminated cylindrical shells are intensively discussed.The English text was polished by Yunming Chen.     

Dynamic energy release rate expression for a spreading circular fracture pattern in a plate

An expression for the dynamic energy release rate of a spreading circular fracture pattern in an uniformly stretched plate is derived from a path-independent energy integral. This is equivalent to the energy dissipated in an incremental growth of a constant velocity circular locus in which the radial tension is zero. The relationship to rapid fracture and multiple crack division becomes apparent as the arc distance separating adjacent crack tips becomes small relative to the radius of the circular locus. The condition at some small fixed distance behind the closely spaced crack tips is then well-stimulated by that of zero radial tension on a circular locus. Experiments could be carried out to establish the accuracy of the analytical dynamic energy release rate expression for multiple crack division.     

Some results for generalized neo-Hookean elastic materials

Several deformations of non-linear elastic materials are used to study the implications of the strain energy density function being dependent only on the first strain invariant. Two kinds of results are obtained, those that compare responses with and without dependence on the second invariant, and those specific to materials whose strain energy functions depend only on the first strain invariant. The deformations are (i) homogenous biaxial extension, (ii) shear superposed on triaxial extension, (iii) inflation of a circular membrane, (iv) circular shear superimposed on a press fit cylinder, (v) torsion of a circular cylinder.