The strongly singular part of h can be determined by recalling that the displacement fields to all bounded energy. An investigation of cracktip stress field criteria for. The first term of the elastic tstresses has also been proven to be an important parameter to characterize the near tip elastic plastic fields of 2d and 3d crack problems on the full set of. Abstractit is shown that if the displacement field and stress intensity factor are known as functions of crack length for any symmetrical load system acting on a linear elastic body in plane strain, then the stress intensity factor for any other symmetrical load system whatsoever on the same body may be directly. Pdf it is shown that if the displacement field and stress intensity factor are known as functions of crack length for any symmetrical load system. The asymptotic stress field near the tip of an antiplane crack lying along a planar bimaterial interface between an elastic and an elastic power law hardening material is analysed. Twoparameter characterization of the neartip stress fields for a bimaterial elasticplastic interface crack z. The results include the crack tip shape and neartip deformation field, and the crack tip opening displacement has been related to a parameter of the applied load, the jintegral.
Finite element analysis of elasticplastic large deformation. The complete range of normal versus shear tractions on the interface at the crack tip is analyzed. Combined mode i and iii cracktip fields 163 i crack i. Thus, the analysis of stresses near the crack tip constitutes an essential part of fracture mechanics.
Pdf some remarks on elastic crack tip stress fields. Based on this solution, a formula for the critical value of jintegral in terms of tstress for an elasticplastic material is derived. The stresses fields near a crack tip of a linear elastic isotropic material for mode i loading are given by. The crack tip stress intensity factors were used to calculate crack growth rates both along the surface and in the through thickness direction using equation 6. More importantly, a sizable plastic strip develops behind the crack tip in the short cracks.
Plot the coordinates x and y in the horizontal plane, and the stresses in the vertical direction. As well known 1, for linear elastic fracture mechanics the presence of a collinear stress only influences the. Crack tip stress and deformation fields are analyzed for tensileloaded ideally plastic crystals. Engineering plasticity from macroscale to nanoscale. The present paper investigates the existing analogies and differences between the tcd and gradient mechanics, the latter formalized according to the so. For a crack in an elasticperfectly plastic crystal, there exist more than one asymptotic stress field around the crack tip. We consider a crack in a rambergosgood solid, as shown in fig. Thus, using the tstress calculated based on the load level and linear elastic material properties to characterize the triaxiality of the cracktip stress state and using the jintegral calculated based on the actual elasticplastic deformation field to measure the scale of the cracktip deformation provides a twoparameter fracture.
Using matlab, the stress fields near a crack tip o. Two subjects of general interest are discussed, namely the asymptotic structure of the crack tip fields, and the appro. Abstractit is shown that if the displacement field and stress intensity factor are known as functions of crack length for any symmetrical load system acting on a. Intrinsic material length, theory of critical distances and. T stress effects on fracture toughness are discussed. Deformation plasticity theory is assumed in the analysis. The stress intensity factor is defined from the elastic stress field equations for a stressed element near the tip of a sharp crack under biaxial or uniaxial. In contrast to the predictions of linear elastic fracture mechanics lefm, the near tip stress fields are dominated by the opening stress which shows a 1r singularity for the neohookean material and a 1r ln r singularity for the exponential hardening solid. The condition governing which field occurs cannot be determined by the asymptotic fields, but depends on external loading conditions. The analysis also includes the calculation of some parameters of in. The characterization of the stress fields near a crack tip for a compact specimen for elasticplastic materials dominated by the plane strain. Request pdf the elastic stress field around a crack tip brittle fracture in a solid in the form of crack growth is governed by the stress field around the crack. There we studied analytically the influence of a uniform porosity distribution on the stress field near a plane strain tensile crack tip in ductile elastic ideally plastic material, assuming that material very near the tip is at yield at all angles about the tip.
I, where r and 8 are the polar coordinates centered at the crack tip. Combined mode i and iii crack tip fields 163 i crack i. Mode i, mode ii, mode iii please note that we use the greek letter to denote the shear modulus, usually written as g, for fear that one might be mistake it for the strain release rate. The axes of orthotropy of both solids are assumed to be parallel to the interface y o. The stressstrain relations for the orthotropic elastic solids may be written in the forms. A series solution is obtained for the elastic plastic crack tip fields. This chapter presents a model of a stress and displacement fields around a rough crack tip in brittle and ductile materials using a prefractal model. A series solution is obtained for the elasticplastic cracktip fields. The hydrostatic stresses near the crack tip are limited due to the lack of constraint on the blunted tip, limiting achievable stress levels except more in a very. Citeseerx some remarks on elastic crack tip stress fields. With a nonsingular plastic zone the velocityfield equations are not uniquely determined by the boundary conditions. Dong and pan 21 carried out an elastic plastic analysis of cracks under planestrain and smallscale yielding. The specific cases of 0 1 o cracks growing in the 1 0 1 direction, and 1 0 1 cracks in the 0, 1, o direction, are considered for both fcc and bcc crystals which flow according to.
Near tip stress and strain fields for short elastic cracks. Elasticplastic stress and strain analysis for fracture mechanics, phase ii. Cracktip fields in elasticplastic material under plane. Some remarks on elastic cracktip stress fields 755 solutions for cracks take the form 19 where the dots stand for terms resulting in nonsingular stresses, where r8 are polar co ordinates centered at the crack tip and where g is a universal function of 8 and also of ratios of elastic moduli 24. New results on the cracktip fields in an elastic powerlaw hardening material under plane stress mode i loading are presented. In this work, two families of asymptotic neartip stress fields are constructed in an elasticideally plastic fcc single crystal under mode i plane strain conditions. Nonsingular plastic stress and velocity fields, for the tip of a crack of finite thickness and root radius, are developed as an elasticplastic crack model that is likely to be more physically realistic than the classical infinitesimal crack with a plastic cracktip singularity. Finite strain stress fields near the tip of an interface. In the present paper, the timedependent crack tip stress fields in an elastic nonlinear viscous body are analyzed for variable load. A ligament field ahead of a crack tip for modeli plane strain problem in a powerlaw hardening material is developed. Neartip stress fields for inplane motions accompanying the propagation of a crack along the interface between two orthotropic elastic solids are considered.
The neartip asymptotic stress fields around an interface crack between an elasticperfectly plastic solid and a rigid substrate are members of a family parameterized by. For a crack in an elastic perfectly plastic crystal, there exist more than one asymptotic stress field around the crack tip. Abstract asymptotic crack tip stress fields are developed for a plane strain crack located on the interface between two incompressible, elasticperfectly plastic solids, with matching elastic properties, but mismatched yield strengths. It is shown that if the displacement field and stress intensity factor are known as functions of crack length for any symmetrical load system acting on a linear elastic body in plane strain, then the stress intensity factor for any other symmetrical load system whatsoever on the same body may be directly determined. Crack tip fields in soft elastic solids subjected to large. Huang department of aerospace and mechanical engineering, the university of arizona, tucson, az 85721. Introduction the socalled tstress, or second term of the williams 1957 series expansion for linear elastic cracktip fields, has found many uses in fracture mechanics. Twoparameter characterization of the neartip stress fields. The paper presents a comprehensive analysis of the stress field near a crack tip for a compact specimen dominated by the plane strain state using the finite element method. Thus, using the t stress calculated based on the load level and linear elastic material properties to characterize the triaxiality of the crack tip stress state and using the jintegral calculated based on the actual elastic plastic deformation field to measure the scale of the crack tip deformation provides a twoparameter fracture. The hydrostatic stresses near the crack tip are limited due to the lack of constraint on the blunted tip, limiting achievable stress levels except more.
Some remarks on elastic cracktip stress fields sciencedirect. Today, it is the critical stress intensity factor k ic, found in the plane strain condition, which is accepted as the defining property in linear elastic fracture mechanics. Tensile cracktip stress fields in elasticperfectly plastic. It is postulated that a twoparameter characterization by k and t or b is needed for the adequate description of the stress and strain field around a short crack. Transactions of the korean society of mechanical engineers, a. The specific cases of 0 1 o cracks growing in the 1 0 1 direction, and 1 0 1 cracks in the 0, 1, o direction, are considered for both fcc and bcc crystals. There we studied analytically the influence of a uniform porosity distribution on the stress field near a plane strain tensile crack tip in ductile elasticideally plastic material, assuming that material very. In elastic bimodular stress field, the integrals due. The elastic stress field around a crack tip 3 brittle fracture in a solid in the form of crack growth is governed by the stress. Some remarks on elastic crack tip stress fields researchgate. It is found that an elastic stress singularity of the order r. The existence of a crack in an otherwise perfect material dramatically amplifies applied stresses to values that approach a mathematical singularity at the cracks tip. It is a theoretical construct usually applied to a homogeneous, linear elastic material and is useful for providing a failure criterion for brittle materials.
Influence of porosity on plane strain tensile cracktip. It is found that the biaxiality ratio would be more negative. The specific cases of 0 1 o cracks growing in the 1 0 1 direction, and 1 0 1 cracks in the 0, 1, o direction, are considered for both fcc and bcc crystals which flow according to the critical resolved shear stress criterion. It is shown that if the displacement field and stress intensity factor are known as functions of crack length for any symmetrical load system acting on a linear.
Tstress in elasticplastic cracktip fields springerlink. Stress field and deformation around a crack tip evaluated by infrared thermography and fracture strength of. The stress intensity factor, is used in fracture mechanics to predict the stress state stress intensity near the tip of a crack or notch caused by a remote load or residual stresses. Near tip fields for a stationary mode iii crack between a. The stress fields formed by a crack transport remotely applied elastic energy to the cracks tip, where the energy is dissipated by material fracture. We show that the shear stress field near the tip is of the formmathematical expression or. New results on the crack tip fields in an elastic powerlaw hardening material under plane stress mode i loading are presented. Finite element study of an interface crack between an elastic.
Thaulow 2 j s1ntef materials technology, n7034 trondheim, norway ntnu, department of machine design. Asymptotic tensile cracktip stress fields in elastic. It is shown that if the displacement field and stress intensity factor are known as functions of crack length for any symmetrical load system acting on a linear elastic body in plane strain, then the stress intensity factor for any other symmetrical load system whatsoever on. Citeseerx northholland tensile crack tip fields in elastic. In the present paper, the timedependent cracktip stress fields in an elasticnonlinear viscous body are analyzed for variable load. To further verify the validity of this postulate, the influence of the third term of the williams series on the stress, strain and displacement fields around the crack tip and in. Nonsingular plastic stress and velocity fields, for the tip of a crack of finite thickness and root radius, are developed as an elastic plastic crack model that is likely to be more physically realistic than the classical infinitesimal crack with a plastic crack tip singularity.
Citeseerx document details isaac councill, lee giles, pradeep teregowda. The effects of small superimposed deformations on the cracktip rate fields are then investigated under mode i and mode ii symmetry conditions. Comparison with detailed fe results for plane strain tension and bend specimens shows that this formulation of the crack. This implies that a yielded region will exist in the material ahead of the crack for all reasonable stress values. A crack subjected to combined mode i and iii elastic k fields along the circumferential boundary. Dec 16, 2008 in contrast to the predictions of linear elastic fracture mechanics lefm, the near tip stress fields are dominated by the opening stress which shows a 1r singularity for the neohookean material and a 1r ln r singularity for the exponential hardening solid. It is a theoretical construct usually applied to a homogeneous, linear elastic material and is useful for providing a failure criterion for brittle materials, and is a critical technique in the discipline of damage tolerance. Crack size limitations for singleparameter characterization are suggested based on a suggested criterion that the stress at a specific distance ahead of the crack should be within 10 percent of the k field. From the results, it is concluded that for slow cycling the cintegral is the load parameter that determines the cracktip fields and therefore the crack growth rate. The stress field near the crack tip is found to consist of a combination of uniform and nonuniform stress regions. From the definition of the stress intensity, based on the elastic stress field near a crack tip, i. Estimation of transient creep cracktip stress fields for seb specimen under elasticplasticcreep conditions. Tensile cracktip stress fields in elasticperfectly plastic crystals y. Note the radial stress discontinuity in plane stress fullyyielded asymptotic crack tip fields in 12,20.
In theory the stress at the crack tip where the radius is nearly zero, would tend to infinity. Elasticplastic crack problems in plane strain and plane stress are discussed. The stress distribution in the neighbourhood of a flat elliptical crack in an elastic solid, proc. Tensile crack tip stress fields in elastic perfectly plastic crystals y. The elastic stress field around a crack tip request pdf. Based on this solution, a formula for the critical value of jintegral in terms of t stress for an elastic plastic material is derived. A family of plane strain crack tip stress fields for. Crack tip stress fields and crack growth under creep fatigue.
Introduction the socalled t stress, or second term of the williams 1957 series expansion for linear elastic crack tip fields, has found many uses in fracture mechanics. From the results, it is concluded that for slow cycling the cintegral is the load parameter that determines the crack tip fields and therefore the crack growth rate. Elastic plastic crack problems in plane strain and plane stress are discussed. Tstress extraction massachusetts institute of technology. Using a generalized asymptotic expansion of the stress function, higherorder terms are found which have newlydiscovered characteristics. An asymptotic analysis of the crack tip stress and deformation field is presented for planestrain tensile cracks in elasticideally plastic single crystals. The characterization of the stress fields near a crack tip. Dong and pan 21 carried out an elasticplastic analysis of cracks under planestrain and smallscale yielding. Perfect plasticity solutions for stationary cracks are recovered upon setting the velocity of propagation of the crack tip equal to zero. The characterization of the stress fields near a crack tip for a. A crack is taken to lie on the 010 plane and its front is aligned along the. The model uses assumed distributions of elastic stresses induced at the elasticplastic boundary via wake contact and compatibility requirements, and defines a set of modified elastic stress intensity factors to characterise the crack stress or displacement tip field. Citeseerx northholland tensile crack tip fields in.
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