In this paper, we first discuss the several known methods to obtain the energy release rate by numerical analysis. After detailed discussions on the path-independent E-integral, we compute the energy release rate at the onset of crack kinking in an infinite medium subjected to a remote inclined load under the anti-plane shear and the plane stress condition ; for such cases, the well-known J-integral is not very useful in obtaining the energy release rate with a high accuracy. Our numerical results agree well with the exact solution for the anti-plane shear condition and also agree well with the published approximate solutions for the plane stress condition.

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In this paper, we compute the energy release rate for the crack across and near the elastic material interfaces by the finite-element method using the path-independent E-integral. In the energy release rate analysis for the crack near the material interfaces, the well-known expressions of the J-integral type cannot be evaluated correctly if the integral path involves a discontinuous material interface ; such cases, in general, require corrective paths or the use of the gradient elements for the discontinuous interface. The E-integral, on the other hand, remains path-independent even for such cases and gives the energy release rate at the onset of the crack kinking for arbitrary directions.

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Tensile fracture tests of specimens having a single blind hole were carried out in order to investigate the mechanism of ductile fracture originating in a surface defect. Although a crack was initiated at the hole edge, the true stress-true strain curve of the holed specimen approximately coincided with that of the plain specimen with no hole untill the true stress reached a maximum value. In the deformation stage of the specimen after this stress value was reached, the growth behavior of the crack was not affected by the deformation of the hole. On the basis of these phenomena, parameter f_ac was defined by the ratio of crack area to minimum cross section of the specimen at which the true stress reached the maximum value, and the effect of hole size on the fracture ductility was examined using the parameter f_ac. The ture strain ε_c at the point of maximum true stress showed good correlation with the parameter f_ac, and the shear mode growth of the crack started unstably at this point. The relation between the fracture ductility ε_f and the parameter fαc was predicted from the relation between ε_c and f_ac and from the growth behavior of the crack. This relation coincided with the experimental results, and it was found that the fracture ductility ε_f of the present experiment is determined mainly by the starting conditions of unstable fracture and the growth behavior of the crack.

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Elastic and elastic-plastic analyses of a crack in a particulate-dispersed functionally graded material (FGM) have been carried out using a newly developed finite element method based on Tohgo-Chou-Weng's (1994, 1995) constitutive relation for particulate-reinforced composites. By setting the mechanical properties of particles and a matrix and their contents graded in the thickness direction, graded and non-graded materials are designed. From comparison of the numerical results for the graded and non-graded materials, the influence of the gradient of the mechanical properties on a stress intensity factor and the crack-tip field is discussed. The following conclusions are derived : ( 1 ) The stress intensity factor of a crack under constant boundary conditions is considerably affected by the gradient of the mechanical properties. ( 2 ) The elastic and plastic stress singular fields around a crack-tip in a FGM are basically described by the fracture mechanics parameters (K_I and J_I) as well as in a non-FGM, using the mechanical properties of the material at the crack tip. ( 3 ) The size of the singular field decreases with an increase in the gradient of the mechanical properties. This means that the applicability of fracture mechanics, such as the small-scale-yielding condition and the validity of the J-integral, is affected by the gradient.

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Mixed-mode fracture toughness for silicon carbide, sialon and mullite was measured using diametral compression tests with a cracked Brazilian disk. Slits introduced by YAG laser in Brazilian disks can be treated as central cracks. The relationships between K_I and K_II for silicon carbide under mixed-mode fracture conditins are consistent with a prediction derived from coplaner energy release rate theory. Experiments on sialon and mullite show that Mode II stress intensity K_IIC is larger than K_IC and Shetty's experimental equation is appropriate for mixed-mode fracture conditions. Observation of fracture surfaces shows that the above differences of fracture conditions depend on the operation of toughning mechanism like grain bridging and grain locking.

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In press forming, fracture of a sheet mostly occurs at a punch corner because the sheet is subjected to severe stretch bending there. The fracture load in stretch bending for sheet metal laminates has been investigated by performing stretch bending tests on a two-ply laminate of aluminum/SUS430 and a three-ply laminate of SUS304/aluminum/SUS430. The results show that the fracture load becomes lower with decreasing die-radius. For a two-ply laminate consisting of weak/strong layers, the fracture load is lower when the weak metal is located at a die side compared to the case of reversed sheet-set condition. An analytical method for the determination of the fracture load has also been presented. The predicted fracture loads are in agreement with the corresponding experimental results.

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This paper presents stress corrosion cracking (SCC) of notched GFRP laminates under an acid environment. Based on a fractographic analysis, it is found that the stress-corrosion cracking a is governed by a breakage of the warp fiber strand. The crack propagation rate is possible to estimate from a microscopic fracture model of the warp fiber strand. To obtain the crack propagation rate, a fracture model is proposed on the basis of some assumptions as follows : ( 1 ) A relation between an applied stress and a mirror zone radius (in the fracture surface of the warp fiber) obeys the Jaras's equation, ( 2 ) Shape of the warp strand's shape is almost an ellipse, ( 3 ) The crack is a self-similar one during the propagation. The crack propagation rate is obtained as a function of the stress intensity factor. It is found that its value agrees the experimental value, and confirmed that the proposed microscopic fracture model is appropriate for evaluating the crack propagation rate in an acid environment.

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Particulate-reinforced aluminum alloy composites, using NiAl intermetallic compound and SiC ceramic particles as the reinforcement phase, were fabricated by a die-casting method. Through high cycle fatigue tests, the fatigue strength of composite materials in the as cast condition was investigated at room and elevated temperatures of 200°C and 300°C. Fatigue strengths of each material gradually decreased with increase of temperature. Composite materials showed a higher fatigue limit, as compared with that of the matrix Al alloy within the tested temperature range. The NiAl particle reinforced material showed a good fatigue limit up to 200°C. At 300°C, the fatigue strength was dominated by the matrix strength. It was found that these fatigue behaviors were associated with the fracture surface observations.

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In this study, a method for calculating the dynamic stress intensity factor of a bimaterial bending specimen with an interface crack is proposed for the first time by making use of a line-spring model. A precracked bending specimen is modeled by one-dimensional beam finite elements and a line-spring representing the stiffness or compliance of a cracked part. The present method enables the one-dimensional analysis of a two -dimensional crack problem ; thus the time variation of dynamic stress intensity factors of a bimaterial bending specimen with an interface crack can be obtained by making use of a personal computer within a few minutes. The results obtained from the present method agree reasonably well with those obtained from the two-dimensional finite element method, although a slight difference in period can be found. The present method enables rapid evaluation of dynamic stress intensity factors. Thus a rapid evaluation system of dynamic fracture toughness of a bimaterial with an interface crack can be achieved by combining an impact test apparatus with a computer program based on the present method which runs on a personal computer.

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This paper is concerned with a theoretical treatment of thermal stress intensity factor for a medium with Kassir's nonhomogeneous material properties. As an analytical model, we consider an infinite body with a penny-shaped crack with radius a subjected to uniform heat flux from the crack surface. Assuming that the thermal conductivity λ, shear modulus of elasticity G and coefficient of thermal expansion α vary with the axial coordinate z according to the relations λ(z)=λ₀(|z/a|+1)^β, G(z)=G₀(|z/a|+1)^m, α(z)=α₀(|z/a|+1)ⁿ, the axisymmetrical steady temperature solution is obtained. Thereafter, the associated thermal stress distribution and the thermal stress intensity factor are evaluated theoretically using the method of superposition. Numerical calculations are carried out for three different cases, and the results are shown in graphical form.

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In order to clarify the radiation pattern of elastic waves from a fluid-filled crack in the earth's crust, dynamic elastic response of a two-dimensional fluid-filled crack is studied, emphasizing the effect of the stiffness due to contact between the asperities on the upper and lower surfaces of the crack. To this end, a singular integral equation is derived for the displacement gap across the crack in the Fourier image space, where the motion of the fluid in the crack is taken into account. The singular integral equation is solved numerically, and the radiation pattern is examined in the intermediate region where the distance from the crack is several ten (10∿30) times the representative length of the crack. It is revealed that the radiation pattern and the amplitude of the elastic waves are governed primarily by the stiffness on the crack surface. The aspect ratio, i. e., the ratio of the crack length to the initial aperture of the crack, has only weak effects except in the case of a crack which is completely open initially.

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Hydraulic fracturing stress measurement technique is the most well-known method for in situ stress measurements. However, a general method has not yet been established for estimating the reliability of the evaluated in situ stress. This paper presents a new method for estimating the reliability of the in situ stress evaluated by hydraulic fracturing stress measurement technique which utilizes a shut-in pressure and an orientation of cracks induced by hydraulic fracturing. The validity of the method was examined by applying it to two sets of artificial data constructed for eight cracks under a given stress state. The shut-in pressure for each crack was given by assuming the shut-in pressure to be equal to the normal stress acting perpendicularly to the crack. It was revealed that the shut-in pressure for each crack was most crucial for obtaining reliable results.

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This paper is concerned with a theoretical treatment of thermal stress and thermal bending problems for a multi-layered anisotropic laminated plate due to partially distributed heat supply. As an analytical model, we consider a laminated rectangular plate consisting of a diagonal pile of layers having orthotropic material properties, i. e. an angle-ply laminate. We obtain the three-dimensional temperature in a transient state and thermal deformation of a simply supported plate using the higher-order shear deformation theory. As an example, numerical calculations are carried out for a 2-layered angle-ply laminate, and the numerical results are examined precisely.

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This study is concerned with the problem of dynamic response of angle-ply laminated cylindrical shells under axial compressive impact loads. A mathematical formulation of shell theory is based on the Kirchhoff-Love hypothesis. Cylindrical shells are analyzed using the Donnell-type equations under the boundary condition for simply supported edges. Subsequently, certain perturbations are superimposed on this motion, and their behavior in time is investigated. The symmetric state of motion of the shell is called stable if the perturbations remain bounded. The solutions for the prebuckling motion and the perturbed motion are obtained using the Galerkin method. The inevitability of dynamically unstable behavior is proved analytically and the effects of various factors, such as compressive load ratio, lamination angle, dynamic unstable mode and dimensions of the cylinder are clarified.

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The stress distributions of single-lap adhesive joints subjected to external bending moments are analyzed as a three-body contact problem by using a two-dimensional theory of elasticity. In the analysis, two similar adherends and an adhesive are replaced by finite strips, respectively. In the numerical calculations, the effects of the ratio of Young's modulus of adherends to that of adhesive and the adhesive thickness on the stress distribution at the interface are examined. As the results, it is found that the stress singularity occurs near the edges of the interface, and the peel stress at the edges of the interface increase with a decrease of Young's modulus of adherends. In addition, photo-elastic experiments are carried out. A fairly good agreement is obtained between the analytical and the experimental results.

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By performing thermomechanical cycling tests on TiNi shape memory alloy, the cyclic properties of the shape memory effect (SME) due to the rhombohedral phase transformation (RPT) and the martensitic transformation (MT) were investigated. The main results are summarized as follows. ( 1 ) In the case of maximum strain in the RPT region, SME does not vary under cyclic deformation. ( 2 ) In the case of maximum strain in the MT region, the MT stress decreases and the MT reverse transformation temperature increases under cyclic deformation. The variation in these properties is large in the early cycles but decreases thereafter and increases markedly if maximum strain is in the MT completion region. ( 3 ) In the case of maximum strain in the MT region, two-way strain, due to RPT, develops under cyclic deformation. If cyclic deformation with maximum strain in the MT completion region is repeated five times, two-way strain of the same amount as that of the RPT strain caused by loading is obtained.

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By introducing a concept of extended plane strain, the dependence of the forming limit strain of sheet metals on their thickness is investigated numerically over the range of in-plane strain ratio α, 0 ≤ α ≤ 1, i.e., the biaxial tension range, using the elastic-plastic finite-element method (E. -P. FEM) whose code's name is GOLDA which was previously developed by one of the authors (Gotoh). The forming limit strain is estimated based on the evolution of the shear band. J2G (J₂-Gotoh's corner theory), which was previously proposed by Gotoh and applied successfully to problems of strain localization such as in the case of shear band, is adopted as the plasticity constitutive equation. It is confirmed that thicker sheets show higher limiting strain, and that such thickness effect becomes weaker for larger α and thicker sheets. Moreover, the forming limit of gradient material sheets (whose mechanical properties vary continuously along the thickness direction of the sheet) is investigated with respect to plane strain tension (α=0) by a similar method to the one above, in which only the distribution of the n-value (the strain-hardening exponent) is varied. Dependence of the shear-band evolution pattern on the n-value distribution pattern is clearly demonstrated. It is concluded that, for the same variation range of n-values, the forming limit increases in the order of ∨-type, simple linear type and ∧-type of n-value distribution through thickness.

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Stress-strain (S-S) relations of a plain woven glass fabric composite were studied under tension-torsion biaxial loadings. Acoustic emissions (AE) were observed. Internal damage of failed specimens was also examined using an optical microscope. Yielding occurred either when the tensile stress component reached the debonding stress of transverse fibers, or when the shear stress component reached the critical stress for initiation of plastic deformation of matrix. A new rectangular yield criterion for initiation of the nonlinear S-S relation of woven fabric composites was proposed based on the experiment. Beyond the yielding point, internal damage affected the S-S relation under shear stress greater than that in normal stress. In the case that the shear stress component was larger than the tensile stress component, fewer AE events occurred. Once AE events were observed, visible internal damage occurred simultaneously and the material soon failed.

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We have developed a computer program which is able to treat three-dimensional information on defects in composite materials. The information on defects was constructed by combining the echo level of the reflector plate method and beam path distance of the pulse reflection method. As an example, the proposed method was applied to GFRP and CFRP laminates including artificial defects. Three-dimensional information on defects was obtained, and the images of defects were visualized by the newly developed computer program. The images generated for defects were so clear that the size and location of each defect could be recognized easily. From these results, it can be shown that the method proposed in this paper is very useful in evaluating defects in composite materials.

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Lekhnitskii solved the stress field around the elastic inclusion in an infinite anisotropic medium under uniform or linearly changing in-plane loads. We expand this study to out-of-plane problems and solve both the stress and displacement field around the elliptical inclusion. This paper shows the errors in Lekhnitskii's formulation. Some numerical examples are given and it is confirmed that our solutions are appropriate.

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This paper presents a unified analysis of isotropic out-of-plane shear problems for infinite elastic bimaterials with a circular elastic inclusion. The applied disturbances considered in this paper are longitudinal shear stress at infinity, concentrated force, screw dislocation, dipole force and dipole dislocation at an arbitrary position. The analysis is based on the complex variable method using the Mobius transformations by Honein and Herrmann. Several numerical examples are given by graphical representations.

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General higher-order approximation theory to analyze static and/or dynamic behaviors of laminated composite structures with interlayer slip is established. Theoretical and accurate characteristics of the theory are clarified by numerical examples. The theory is established by using modified Hamilton's principle for relaxed displacement continuity requirement, after expanding displacements of each lamina using power series of the thickness coordinate. The independent unknown variables of this theory are the displacement coefficients of each lamina and interlamina stresses. It is shown that the present theory includes the previous theories, and improves the defects of those theories.

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The semi-discrete method of arbitrary lines (MAL) is a general dimensional reduction approach for partial differential equations over arbitrary domains by solving systems with boundary value problems for ordinary differential equations. In this study, we first give a MAL formulation of 2-dimensional elastoplastic problems. The application of the MAL to plasticity analysis has a problem in treating the discontinuity of the coefficients of governing equations at the elastic-plastic boundary. We propose a method which approximates the discontinuity of the coefficients by smooth curve, e.g., splines. Based on this method, we obtain a valid MAL formulation for elastoplastic problems, and demonstrate its effectiveness and accuracy on a typical problem.

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Constitutive models to describe a coupling between deformation and damage due to creep of polycrystalline metallic materials are discussed from phenomenological and continuum mechanics points of view. The constitutive modeling is based on the irreversible thermodynamics for internal state variable theories, where the thermodynamic potentials, i. e., free energy and dissipation energy functions, are defined using hardening and damage variables. The material damage is assumed to be isotropic. First, a new damage-coupled kinematic-hardening model is developed in the invariant form on the basis of the Malinin-Khadjinsky model. The evolution equation of the hardening variable is prescribed by the Bailey-Orowan format which includes the effects of isotropic damage. Then, an isotropic-hardening model taking damage into consideration is formulated by assuming a particular representation of the kinematic hardening variable. The evolution equation of the isotropic creep damage is analogous to that developed by Kachanov and Rabotnov. However, it takes into account a coupling with creep hardening and softening. The present models can describe primary, secondary and tertiary creep behavior, and they are applicable to variable loading conditions. The creep rupture time predicted, even in the simplest case, depends on the time and degree of damage at which the hardening variable reaches its saturation state under the applied stress conditions.

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