The strain energy density ratio criterion for predicting cracking direction in composite materials

The strain energy density ratio criterion for predicting cracking direction incomposite materials is proposed.The Tsai-Hill criterion and Norris criterion ofcomposite materials are extended to predict the cracking direction in composites.Thethree criteria are used to analyse the crack propagation problem of the unidirectionalfibre composite sheet with various fibre directions.The predicted results are comparedwith those of the existing normal stress ratio criterion and strain energy densitycriterion.     

EVALUATION OF DUCTILE FRACTURE CRITERIA IN A GENERAL THREE-DIMENSIONAL STRESS STATE CONSIDERING THE STRESS TRIAXIALITY AND THE LODE PARAMETER

This paper is concerned with evaluation of various ductile fracture criteria in a general three-dimensional stress state of stress triaxiality, the Lode parameter and the equiva- lent plastic strain to fracture. Evaluation is carried out by comparing fracture loci constructed by fracture criteria to experimental results of A12024-T351. Comparison demonstrates that the Modified Mohr-Coulomb criterion and a newly proposed criterion provide sufficient predictabil- ity of fracture strain. Moreover, evaluation is emphasized on the predicted cut-off value for stress triaxiality. The evaluation demonstrates that the Cockcroft-Latham, Brozzo, Oh, Ko-Huh and the new criteria coupled a reasonable cut-off value for ductile materials.     

Incubation time fracture criterion for FEM simulations

The paper is discussing problems connected with embedment of the incubation time criterion for brittle fracture into finite element computational schemes.Incubation time fracture criterion is reviewed;practical questions of its numerical implementation are extensively discussed.Several examples of how the incubation time fracture criterion can be used as fracture condition in finite element computations are given.The examples include simulations of dynamic crack propagation and arrest,impact crater formation(i.e.fracture in initially intact media),spall fracture in plates,propagation of cracks in pipelines.Applicability of the approach to model initiation,development and arrest of dynamic fracture is claimed.     

A MOVING CRACK IN A NONHOMOGENEOUS MATERIAL STRIP

This paper considers an anti-plane moving crack in a nonhomogeneous material strip of finite thickness. The shear modulus and the mass density of the strip are considered for a class of functional forms for which the equilibrium equation has analytical solutions. The problem is solved by means of the singular integral equation technique. The stress field near the crack tip is obtained. The results are plotted to show the effect of the material non-homogeneity and crack moving velocity on the crack tip field. Crack bifurcation behaviour is also discussed. The paper points out that use of an appropriate fracture criterion is essential for studying the stability of a moving crack in nonhomogeneous materials. The prediction whether the unstable crack growth will be enhanced or retarded is strongly dependent on the type of the fracture criterion used. Based on the analysis, it seems that the maximum 'anti-plane shear' stress around the crack tip is a suitable failure criterion for moving cracks in nonhomogeneous materials.     

A continuous-discontinuous cellular automaton method for cracks growth and coalescence in brittle material简

A method of continuous-discontinuous cellular automaton for modeling the growth and coalescence of multiple cracks in brittle material is presented. The method uses the level set to track arbitrary discontinuities, and calculation grids are independent of the discontinuities and no remeshing are required with the crack growing. Based on Grif- fith fracture theory and Mohr-Coulumb criterion, a mixed fracture criterion for multiple cracks growth in brittle mate- rial is proposed. The method treats the junction and coales- cence of multiple cracks, and junction criterion and coales- cence criterion for brittle material are given, too. Besides, in order to overcome the tracking error in the level set ap- proximation for crack junction and coalescence, a dichotomy searching algorithm is proposed. Introduced the above the- ories into continuous-discontinuous cellular automaton, the present method can be applied to solving multiple crack growth in brittle material, and only cell stiffness is needed and no assembled global stiffness is needed. Some numerical examples are given to shown that the present method is efficient and accurate for crack junction, coalescence and percolation problems.     

Exact solutions of two semi-infinite collinear cracks in piezoelectric strip

Using the complex variable function method and the conformal mapping technique,the fracture problem of two semi-infinite collinear cracks in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load on the partial crack surface.Analytic solutions of the field intensity factors and the mechanical strain energy release rate are derived under the assumption that the surfaces of the crack are electrically impermeable.The results can be reduced to the well-known solutio...     

A MIXED MODE FRACTURE CRITERION BASED ON THE MAXIMUM TANGENTIAL STRESS IN BRITTLE INCLUSION

A closed-form solution for predicting the tangential stress of an inclusion located in mixed mode Ⅰ and Ⅱ crack tip field was developed based on the Eshelby equivalent inclusion theory. Then a mixed mode fracture criterion, including the fracture direction and the critical load, was established based on the maximum tangential stress in the inclusion for brittle inclusioninduced fracture materials. The proposed fracture criterion is a function of the inclusion fracture stress, its size and volume fraction, as well as the elastic constants of the inclusion and the matrix material. The present criterion will reduce to the conventional one as the inclusion having the same elastic behavior as the matrix material. The proposed solutions are in good agreement with detailed finite element analysis and measurement.     

SIF-based fracture criterion for interface cracks

The complex stress intensity factor K governing the stress field of an interface crack tip may be split into two parts, i.e.,■ and s~(-iε), so that K = ■ s~(-iε), s is a characteristic length and ε is the oscillatory index. ■ has the same dimension as the classical stress intensity factor and characterizes the interface crack tip field. That means a criterion for interface cracks may be formulated directly with■, as Irwin(ASME J. Appl. Mech. 24:361–364, 1957) did in 1957 for the classical fracture mechanics. Then, for an interface crack,it is demonstrated that the quasi Mode I and Mode II tip fields can be defined and distinguished from the coupled mode tip fields. Built upon SIF-based fracture criteria for quasi Mode I and Mode II, the stress intensity factor(SIF)-based fracture criterion for mixed mode interface cracks is proposed and validated against existing experimental results.     

ON PATH-INDEPENDENT INTEGRALS AND FRACTURE CRITERIA IN NONLINEAR FRACTURE DYNAMICS

In this paper,we consider path-independent integrals and frac-ture criteria in nonlinear fracture dynamics.The dynamic effectand crack propagation are included in the discussion.Both nonlinearelastic and elastic-plastic case for crack propagation have been con-sidered.and the related path-independent integrals are proposed.Asan example,the steady state propagation of crack has been discussed.Lastly,we give the mechanical meaning of this path-independent inte-grals as the crack extension force,and make it possible to use thepath-independent integrals(as fracture criterion in nonlinear frac-ture dynamics).     

INFLUENCE OF LOADING RATE ON DYNAMIC FRACTURE BEHAVIOR OF FIBER-REINFORCED COMPOSITES

The effect of loading rate on the dynamic fracture properties and the failure mechanisms of glass fiber-reinforced composite materials under mode I fracture is studied. Dynamic reflective caustic experiments are carried out for two loading rates. By measuring the characteristic dimensions of the shadow spots during the caustic experiments, the dynamic SIFs are calculated for different loading rates. The experimental results indicate that the dynamic fracture toughness Kid increases remarkably with increasing loading rate, and the crack grows faster under the high-velocity impact. Moreover, by examining the crack growth routes and the fracture surfaces, it is shown that the loading rate also greatly affects the failure mechanisms at micro-scale.     

PREDICTION OF MODE Ⅰ CRACK PROPAGATION DIRECTION IN CARBON-FIBER REINFORCED COMPOSITE PLATE

A newly developed Z fracture criterion for the composite materials was introduced,the new concepts of in-plane average strain,in-plane dilatational strain energy density factor and reciprocal characteristic function were presented.Many experimental results show that the Z fracture criterion can be well used to predict the crack propagating direction for mode Ⅰ crack in carbon-fiber reinforced composite laminates.     

Magneto-electro-elastic antiplane analysis of a bimaterial BaTiO3–CoFe2O4 composite wedge with an interface crack

The antiplane analysis is made for a bimaterial BaTiO₃–CoFe₂O₄ composite wedge containing an interface crack. The coupled magneto-electro-elastic field is induced by the piezoelectric/piezomagnetic BaTiO₃–CoFe₂O₄ composite materials. For the crack problems, the intensity factors of stress, strain, electric displacement, electric field, magnetic induction and magnetic field at crack tips are derived analytically. Also, the energy density criterion is applied to predict the fracture behavior of the interface crack. The numerical results also show that the energy release rate for a crack in a single wedge is negative.     

广义平均形状改变能密度断裂准则及应用

基于形状改变能为材料起裂扩展控制参量的物理事实及裂纹尖端断裂控制区能量平均概念,提出了计及裂纹尖端应力场特征级数展开奇异项和常数项的广义平均形状改变能密度(GADSED)准则,建立了I-II-III 混合型裂纹断裂判据计算式,为工程结构疲劳断裂评估提供了新选择．基于提出的GADSED 准则,系统分析了T应力对裂纹断裂判据的影响,结果表明：当参数|Ba|数值相同时：负值T应力的I-II 混合型裂纹更易起裂扩展,正值T应力的KΙf值高于负值T应力的KΙf值,正负T应力的KIIf值相同;T应力在区间0 < Bα < 0.45 时增大了KΙf值（3 %以内）,T应力降低了KIIf值．根据GADSED 准则完成了双轴疲劳载荷平板表面I 型裂纹扩展寿命预报,结果表明：基于GADSED 准则的裂纹扩展寿命预报值约为传统方法预报值的40.7 %,可为工程实际评估提供借鉴．     

Magnetoelectroelastic composite with poling parallel to plane of line crack under out-of-plane deformation

The three-dimensional field equations can in general be regarded as the sum of in-plane and out-of-plane deformation. The method for the general solution is the same for both although the boundary conditions could make a difference. If a particular solution in exact form may be found for the out-of-plane case, the same may not hold for the in-plane case. Hence, there may be a good reason for discussing the out-of-plane crack problem in certain situations that should be emphasized. Otherwise, the reason may lie in the exploration of possible application to the in-plane problem, a direct solution of which would have required a considerable effort. The contribution of this work rests on the new findings for the case of poling parallel to the crack in a magnetoelectroelastic composite made of BaTiO₃–CoFe₂O₄. The inclusions are BaTiO₃ and the matrix is CoFe₂O₄. Several new features of the solution were not expected before hand.Unlike in-plane deformation with poling normal to the crack plane, maximum crack growth enhancement is found to occur in the BaTiO₃–CoFe₂O₄ composite for a volume fraction of about 50%. Crack retardation increases as the volume fraction of the inclusions either increase or decrease. The occurrence of this same phenomenon in Mode I and II remain to be investigated. Poling direction of magnetic and electric field for line defects can have a significant effect on crack growth for magnetoelectroelastic materials. The foregoing conclusions are based on predictions made from the strain energy density criterion.     

A MODE Ⅱ CRACK IN A TWO-DIMENSIONAL OCTAGONAL QUASICRYSTALS

The present study develops the fracture theory for a two-dimensional octagonal quasicrystals. The exact analytic solution of a Mode Ⅱ Griffith crack in the material was obtained by using the Fourier transform and dual integral equations theory, then the displacement and stress fields, stress intensity factor and strain energy release rate were determined, the physical sense of the results relative to phason and the difference between mechanical behaviors of the crack problem in crystal and quasicrystal were figured out. These provide important information for studying the deformation and fracture of the new solid phase.     

MAXIMAL ELEMENTS FOR GB-MAJORIZED MAPPINGS IN PRODUCT G-CONVEX SPACES AND APPLICATIONS (Ⅰ)

A new family of set-valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several existence theorems of maximal elements for the family of set-valued mappings were proved under noncompact setting of product generalized convex spaces. These theorems improve, unify and generalize many important results in recent literature. Contributed by DING Xie-ping Foundation items: the National Natural Science Foundation of China (19871059); the Natural Science Foundation of Education Department of Sichuan Province of China ([2000]25) Biography: DING Xie-ping (1938∼)     

Conservation Law and Application of J-Integral in Multi-Materials

The conservation law of J-integral in two-media with a crack paralleling to the interface of the two media was firstly proved by analytical and numerical finite element method. Then a schedule model was established that an interface crack is inserted in four media. According to the J-integral conservation law on multi-media, the energy release ratio of Ⅰ-type crack was considered to be conservation when the middle medium layers are very thin. And the conservation law was also convinced by numerical method. By means of the dimension analysis on the model, the asymptotic results and formula calculating the energy release ratio and complex stress intensity factor are presented.     

MAXIMAL ELEMENTS FOR G-B-MAJORIZED MAPPINGS IN PRODUCT G-CONVEX SPACES AND APPLICATIONS (Ⅱ)

By applying existence theorems of maximal elements for a family of G_B-majorized mappings in a product space of G-convex spaces, some coincidence theorem, Fan-Browder type fixed point theorem and some existence theorems of solutions for a system of minimax inequalities are proved under noncompact setting of G-convex spaces. These theorems improve and generalize many important known results in literature. Contributed by Duping Xie-ping Foundation items: the National Natural Science Foundation of China (19871059); the Natural Science Foundation of Education Department of Sichuan Province ([2000]25) Biography: Duping Xie-ping (1938∼), Professor (E-mail: dingxip@sichu.edu.cn)     

Some problems in the Z-C-X space

The new concepts of the Z-C-X space and excellent cone are introduced. Some problems of random semiclosed 1-set-contractive operator are investigated in the Z-C-X space. At first, an important inequality is proved. Secondly, several new conclusions are proved by means of random fixed point index in the theory of random topological degree. A random solution of a class of random operator equations under conditions of imitating the parallelogram law is obtained, famous Altman’s theorem is generalized in partially ordered Z-C-X space. Therefore, some new results are obtained.