ON J-INTEGRALS NEAR MODELS Ⅰ,Ⅱ CRACK TIPS IN THE PLATE OF ORTHOTROPIC COMPOSITE MATERIAL

In this paper, we prove the independence of the path of the imegrals near model i II track tips in the plate of the orthotropic composite material. Then we derive the computing formulae of the J-integrals at the cases of and by using a complex variable method and redueing J-imegrals to compley farmThe J-integral computational formulae derived this paper have certain reference value for the theoretical researches and the experimental verifications in the plane fracture for composite material.

ON J-INTEGRALS IN THE PLANE FRACTURE OF COMPOSITE MATERIALS

By using a complex function method in this paper, the complex form of J-integral of mixed mode crack tip for unidirectional plate of linear-elastic orthotropic composites is obtained first by substituting crack tip stresses and displacements into general formula of J-integral. And then, the path-independence of this J-integral is proved. Finally, the computing formula of this J-integral is derived. As special examples, the complex forms, path-independence and computing formulae of J-integrals of mode I and mode II crack tips for unidirectional plate of linear-elastic orthotropic composites are given.

CRACK TIP FIELD AND J-INTEGRAL WITH STRAIN GRADIENT EFFECT

The mode I plane strain crack tip field with strain gradient effects is presented in this paper based on a simplified strain gradient theory within the framework proposed by Acharya and Bassani.The theory retains the essential structure of the incremental version of the conventional J_2 deformation theory.No higher-order stress is introduced and no extra boundary value conditions beyond the conventional ones are required.The strain gradient effects are considered in the constitutive relation only through the instantaneous tangent modulus.The strain gradient measures are included into the tangent modulus as internal parameters.Therefore the boundary value problem is the same as that in the conventional theory.Two typical crack problems are studied:(a)the crack tip field under the small scale yielding condition induced by a linear elastic mode-I K-field and(b)the complete field for a compact tension specimen.The calculated results clearly show that the stress level near the crack tip with strain gradient effects is considerable higher than that in the classical theory.The singularity of the strain field near the crack tip is nearly equal to the square-root singularity and the singularity of the stress field is slightly greater than it.Consequently,the J-integral is no longer path independent and increases monotonically as the radius of the calculated circular contour decreases.

PATH-INDEPENDENT J-INTEGRAL AND ITS DUAL FORM IN ELASTIC-PLASTIC SOLIDS WITH FINITE DISPLACEMENTS

In this paper, based on energy variational principles of elastic-plastic solids, the path-independent J-integral and its dual form in elastic-plastic solids with finite displacements are presented. Whose testification is given there after.

Theory and Calculation of the J-Integral for Coupled Chemo-Mechanical Fracture Mechanics

In this paper,by introducing a chemical field,the J-integral formulation is presented for the chemo-mechanical coupled medium based on the laws of thermodynamics.A finite element implementation of the J-integral was performed to study the mode I chemo-mechanical coupled fracture problem.For derivation of the coupled J-integral,the equivalent domain integral(EDI)method was applied to obtain the mode I J-integral,with expression of the area integrals based on constitutive relationships of a linear elastic small deformation for chemo-mechanical coupling,instead of the finite deformation problem.A finite element procedure is developed to compute the mode I J-integral,and numerical simulation of the y-direction stress field is studied by a subroutine UEL(User defined element)developed in ABAQUS software.Accuracy of the numerical results obtained using the mode I J-integral was verified by comparing them to a well-established model based on linear elastic fracture mechanics(LEFM).Furthermore,a numerical example was presented to illustrate path-independence of the formulated J-integral for a chemo-mechanical coupled specimen under different boundary conditions,showing a high accuracy and reliability of the present method.The variation laws of J-integral and the y-direction stress field with external chemical,mechanical loading and time are revealed.The J-integral value increases with larger external concentration loading in the same integral domain.The extent of diffusion is much greater with larger concentration,which leads to a stronger coupling effect due to the chemical field.This work provides new insights into the fracture mechanics for the chemo-mechanical coupled medium.

A NEW CYCLIC J-INTEGRAL FOR LOW-CYCLE FATIGUE CRACK GROWTH

The constitutive equation under the low-cycle fatigue （LCF） was discussed, and a two-dimensional （2-D） model for simulating fatigue crack extension was put forward in order to propose a new cyclic J-integral. The definition, primary characteristics, physical interpretations and numerical evaluation of the new parameter were investigated in detail. Moreover, the new cyclic J-integral for LCF behaviors was validated by the compact tension （CT） specimens. Results show that the calculated values of the new parameter can correlate well with LCF crack growth rate, during constant-amplitude loading. In addition, the phenomenon of fatigue retardation was explained through the viewpoint of energy based on the concept of the new parameter.

A J-INTEGRAL ANALYSIS OF CRACKS IN OVERMATCHED WELDED JOINTS

The effects of material inhomogeneity and weld width of the overmatched welded joints with a longitudinal crack or flaw upon the J-interal,a characterizing parameter for elastoplastic fracture,have been studied.The overmatched weld is idealized to be a parallelly cracked and sandwiched hard layer,the yieht stress of which is higher than that of the base metal.Numeri- cal solutions were obtained by using elastoplastic finite element method under the assumption of plane stress.The resuits show that the values of J-integral are remarkably affected by the material inhomogeneity ant the weld width especially when the nominal stress or nominal strain is comparatively high,which,therfore,should be taken into account when evaluating the crack driving force for an overmatched joint.

STUDY ON DYNAMIC J-INTEGRAL OF MECHANICAL HETEROGENEOUS WELDED JOINT

Welded joint is a mechanical heterogeneous body, and mechanical heterogeneity has great effect on dynamic fracture behaviour of welded joints. In the present investigation, dynamic response curve and dynamic J-integral of practical undermatched welded joint and whole base and whole weld three-point-bend (TPB) models containing longitudinal crack are com- puted. Dynamic J-integral is evaluated using virtual crack extension (VCE) method and the computation is performed using MARC finite element code. Because of the effect of inertia, dynamic load response curve of computed model waves periodically. Dynamic J-integral evaluated by VCE method is path independent. The effect of inertia has little influence on dynamic J-integral curve. The value of dynamic J-integral of undermatched welded joint is lower than that of whole base metal and higher than that of whole weld metal. The results establish the foundation of safety evaluation for dynamic loaded welded structures.

An extended J-integral for evaluating fluid-driven cracks in hydraulic fracturing

J-integral has served as a powerful tool in characterizing crack tip status. The main feature, i.e. path- independence, makes it one of the foremost fracture parameters. In order to remain the path- independence for fluid-driven cracks, J-integral is revised. In this paper, we present an extended J-in- tegral explicitly for fluid-driven cracks, e.g. hydraulically induced fractures in petroleum reservoirs, for three-dimensional （3D） problems. Particularly, point-wise 3D extended J-integral is proposed to char- acterize the state of a point along crack front. Besides, applications of the extended J-integral to porous media and thermally induced stress conditions are explored. Numerical results show that the extended J- integral is indeed path-independent, and they are in good agreement with those of equivalent domain integral under linear elastic and elastoplastic conditions. In addition, two distance-independent circular integrals in the K-dominance zone are established, which can be used to calculate the stress intensity factor （SIF）.

THE FULLY PLASTIC J-INTEGRAL OF CORNER CRACKS AT A HOLE IN A PLATE

The line-spring model of surface cracks is applied to the fully plastic analysis of corner cracks at a hole in a plate. The generalized fully plastic constitutive relations and the fully plastic J-integral, as well as its coefficients in polynomial expressions are given. The model obtained is incorporated into a finite element program. The corner cracks at a hole in a plate subjected pure tensions are calculated by the present model. The fully plastic J-integral is then estimated. The results obtained show that the line-spring model is effective for the analysis of corner cracks. The influence of the crack depth and the hardening exponent on the fully plastic J-integral is also discussed.

RELATIONSHIP BETWEEN J-INTEGRAL AND FRACTURE SURFACE AVERAGE PROFILE

To investigate the causes that led to the formation of cracks in materials, a novel method that only considered the fracture surfaces for determining the fracture toughness parameters of J-integral for plain strain was proposed The principle of the fracture-surface topography analysis （FRASTA） was used. In FRASTA, the fracture surfaces were scanned by laser microscope and the elevation data was recorded for analysis. The relationship between J-integral and fracture surface average profile for plain strain was deduced. It was also verified that the J-integral determined by the novel method and by the compliance method matches each other well.

STUDY ON THE RELATIONSHIP BETWEEN J-INTEGRAL AND COD

J-integral arid crack opening displacement 8 （COD） were important parameters for characterization of fractures in engineering materials. The relationship between J-integral arid COD has been investigated for a long time and was generally represented as J = m σy, δ, where σy is the yield strength arid m is a function of specimen geometry arid material properties. To determine the value of m, extensive studies and experiments have been performed. The method that used the fracture-surface topography analysis （ FRASTA ） for determining J-integral from fracture surfaces of materials was introduced. On the basis of the relationship between COD arid fracture surface average profile, the relationship between J-integral arid COD was deduced arid compared with the generally used equation. The method was experimentally confirmed to be able to provide a new way to determine the relationship between J-integral and COD.

A STUDY OF J-INTEGRAL OF THE ORTHOTROPIC COMPOSITE MATERIAL

The relation between J-integral near model I crack tip in the orthotropic plateand displacement derivative is derived in this paper. Meanwhile,Ihe relation betweenstress intensity factor K_1 and displacement is also given in this paper.With stickingfilm moire interferometry method, the three-point bending beam is tested,thus thevalues of J-integral and K_1 can be obtained.from the displacement field,and then thetruth of relation formula between J-integral and K_1 in the orthotrtopic compositematerials is experimentally verified.

A CATASTROPHE ANALYSIS ON THE STABILITY OF THE CRACK GROWTH IN THREE-POINT BENDING SPECIMENS

This paper presents an attempt at the application of catastrophe theory to the stability analysis of J-controlled crack growth in three-point bending specimens. By introducing the solutions of J-integral in the completely yielding state for the ideal plastic material, the critical condition of losing stability for the crack propagation in the specimen is obtained, based on the cusp catastrophe theory. The process of the crack growth from geometrical sense is described.

A Pipeline Fracture Model of Hydrogen-induced Cracking

The relationship between hydrogen concentration and crack tip stress, strain field, hydrogen diffusion and internal pressure respectively in the crack tip process zone was investigated, and the length of the crack tip process zone of hydrogen-induced cracking （HIC） was determined. Based on the mechanism of fracture of micro-crack nucleation, a dislocation model was presented for the fracture criteria of HIC. The influence factors of pipeline tube fracture ductile KISCC in the presence of hydrogen was analyzed, and the critical pressure bearing capability of a pipeline with hydrogeninduced cracking and the critical J-integrity （JISCC） were calculated, which is very important for pipeline safety.

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.

Mechanical characterization of sisal reinforced cement mortar

This work aims at evaluating the mechanical behavior of sisal fiber reinforced cement mortar. The composite material was produced from a mixture of sand, cement, and water. Sisal fibers were added to the mixture in different lengths. Mechanical characterization of both the composite and the plain mortar was carried out using three point bend, compression, and impact tests. Specimens containing notches of different root radii were loaded in three point bending in an effort to determine the effect of the fibers on the fracture toughness of the material. The results obtained indicate that, while fiber reinforcement leads to a decrease in compressive strength, J-integral calculations at maximum load for the different notch root radii have indicated, particularly for the case of long fibers, a significant superiority of the reinforced material in comparison with the plain cement mortar, in consistence with the impact test data.

The energy release rate for hygrothermal coupling elastic materials

In the fracture problems of hydrophilic elastic materials under coupling effects of heat conduction, moisture diffusion and mechanical deformation, the conventional J-integral is no longer path independent. The value of J is unequal to the energy release rate in hygrothermal coupling cases. In the present paper, we derived a general form of the energy release rate for hygrothermal fracture problems of the hydrophilic elastic materials on the basis of energy balance equation in cracked areas. By introducing the constitutive relations and the essential equations of irreversible thermodynamics, a specific expression of the energy release rate was obtained, and the expression can be reformmulated as path independent integrals, which is equivalent to the energy release rate of the fracture body. The path independence of the integrals is then verified numerically.

Energy Release Rates for Interface Cracks in Multilayered Structures

This paper examines the evolution of the interfacial deflection energy release rates in multilayered structures under four-point bending.The J-integral and the extended finite element method(XFEM)are adopted to investigate the evolution of the interfacial deflection energy release rates of composite structures.Numerical results not only verify the accuracy of analytical solutions for the steady-state interfacial deflection energy release rate,but also provide the evolutionary history of the interfacial deflection energy release rate under different crack lengths.In addition,non-dimensional parametric analyses are performed to discuss the effects of normalized ratios of the crack length,the elastic modulus,and the thickness on the interfacial deflection energy release rate.The results demonstrate that the elastic modulus ratio and thickness ratio have a distinct influence on the interfacial deflection energy release rate for multilayered beams.Furthermore,an unstable interfacial crack tends to occur for elastic multilayer beams with higher elastic modulus on the upper sub-beam under bending moments.The unstable interfacial fracture shows a decreasing interfacial deflection energy release rate with an increasing interfacial crack length.

FURTHER INVESTIGATION OF INTERACTION BETWEEN INTERFACE MACROCRACK AND PARALLEL MICROCRACKS IN BIMATERIAL ANISOTROPIC SOLIDS

In this paper, with the aid of superimposing technique and the Pseudo Traction Method (PTM), the interaction problem between an interface macrocrack and parallel microcracks in the process zone in bimaterial anisotropic solids is reduced to a system of integral equations. After the integral equations are solved numerically, a conservation law among three kinds ofJ-integrals is obtained which are induced from the interface macrocrack tip, the microcrack and the remote field, respectively. This conservation law reveals that the microcrack shielding effect in such materials could be considered as the redistribution of the remoteJ-integral.