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Journal ArticleDOI

On the relationship between critical tensile stress and fracture toughness in mild steel

TL;DR: In this paper, the critical value of tensile stress (a) for unstable cleavage fracture to the fracture toughness (K,,) for a high-nitrogen mild steel under plane strain conditions.
Abstract: SUMMARY AN ANALYSIS is presented which relates the critical value of tensile stress (a,) for unstable cleavage fracture to the fracture toughness (K,,) for a high-nitrogen mild steel under plane strain conditions. The correlation is based on (i) the model for cleavage cracking developed by E. Smith and (ii) accurate plastic*lastic solutions for the stress distributions ahead of a sharp crack derived by J. R. Rice and co-workers. Unstable fracture is found to be consistent with the attainment of a stress intensification close to the tip such that the maximum principal stress a,, exceeds a, over a characteristic distance, determined as twice the grain size. The model is seen to predict the experimentally determined variation of K,, with temperature over the range -150 to -75°C from a knowledge of the yield stress and hardening properties. It is further shown that the onset of fibrous fracture ahead of the tip can be deduced from the position of the maximum achievable stress intensiiication. The relationship between the model for fracture ahead of a sharp crack, and that ahead of a rounded notch, is discussed in detail.
Citations
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Journal ArticleDOI
TL;DR: In this article, the authors compared the size, shape and orientation of the holes which cause failure initiation with the isotropic continuum analysis of F.A. Mc Clintock (1968), with particular reference to the effects of directionality and stress state on the condition for flow localization to occur between holes.
Abstract: The strain required to initiate ductile failure in three low-alloy, quenched and tempered steels has been determined in multi-axial stress-states. The ductility was found to depend markedly both on the orientation of the stress system with respect to the rolling direction and on the tri-axiality of the stress-state. In some cases, ductile failure occurred at plastic strains which were only a few times the yield strain. Metallographic studies have been used to compare the size, shape and orientation of the holes which cause failure initiation with the isotropic continuum analysis of F.A. Mc Clintock (1968). The application of ductile-fracture models to directional steels is discussed with particular reference to the effects of directionality and stress-state on the condition for flow localization to occur between holes.

1,282 citations

Journal ArticleDOI
TL;DR: In this article, a local criterion based on Weibull theory was proposed to determine the mechanical conditions for cleavage fracture at the crack tip of A508 class 3 steel, and the results can be accounted for in terms of the local criterion which takes into account the effect of plastic strain.
Abstract: Experiments were performed on three heats of A508 class 3 steel in order to determine the mechanical conditions for cleavage fracture. These tests were carried out on various geometries including 4-point bend specimens and axisymmetric notched tensile bars with different notch radii which have been modelized using the finite element method. In one heat, the temperature range investigated was from 77 K to 233 K. It is shown that the cleavage resistance is increased by tensile straining. Moreover, the probability of fracture obeys the Weibull statistical distribution. All the results can be accounted for in terms of a local criterion based on Weibull theory and which takes into account the effect of plastic strain. In this criterion, the parameters which were experimentally determined are found to be temperature independent over the range 77 K to 170 K. The applicability of the approach proposed for cleavage fracture at the crack tip is also examined. It is shown that the experimental results published in the literature giving the variation of fracture toughness with temperature can be explained by the proposed criterion which predicts reasonably well both the scatter in the experimental results and theKICtemperature dependence.

1,090 citations

Book ChapterDOI
TL;DR: In this paper, a convected coordinate formulation of the field equations is used to describe the material failure by coalescence of microscopic voids, and a detailed micromechanical study of shear band bifurcation that accounts for the interaction between neighboring voids and the strongly nonhomogeneous stress distributions around each void has been carried out, and also elaborated in this chapter.
Abstract: Publisher Summary This chapter describes the material failure by coalescence of microscopic voids. The voids nucleate mainly at second phase particles, by decohesion of the particle-matrix interface or by particle fracture, and subsequently the voids grow because of plastic straining of the surrounding material. The growth of voids to coalescence by plastic yielding of the surrounding material involves so large geometry changes that finite strain formulations of the field equations are a necessary tool. A convected coordinate formulation of the governing equations is used. Convected coordinates are introduced, which serve as particle labels. The convected coordinate net can be visualized as being inscribed on the body in the reference state and deforming with the material. It is found that after nucleation, cavities elongate along the major tensile axis and that two neighboring cavities coalesce when their length has grown to the order of magnitude of their spacing. This local failure occurs by the development of slip planes between the cavities or simply necking of the ligament. A detailed micromechanical study of shear band bifurcation that accounts for the interaction between neighboring voids and the strongly nonhomogeneous stress distributions around each void has been carried out, and are also elaborated in this chapter.

938 citations

Journal ArticleDOI
TL;DR: In this article, a finite element method was used to analyze the deformation field around smoothly-blunting crack tips in both non-hardening and hardening elastic-plastic materials, under contained plane-strain yielding and subject to mode I opening loads.
Abstract: A nalyses of the stress and strain fields around smoothly-blunting crack tips in both non-hardening and hardening elastic-plastic materials, under contained plane-strain yielding and subject to mode I opening loads, have been carried out by use of a finite element method suitably formulated to admit large geometry changes. The results include the crack-tip shape and near-tip deformation field, and the crack-tip opening displacement has been related to a parameter of the applied load, the J -integral. The hydrostatic stresses near the crack tip are limited due to the lack of constraint on the blunted tip, limiting achievable stress levels except in a very small region around the crack tip in power-law hardening materials. The J -integral is found to be path-independent except very close to the crack tip in the region affected by the blunted tip. Models for fracture are discussed in the light of these results including one based on the growth of voids. The rate of void-growth near the tip in hardening materials seems to be little different from the rate in non-hardening ones when measured in terms of crack-tip opening displacement, which leads to a prediction of higher toughness in hardening materials. It is suggested that improvement of this model would follow from better understanding of void-void and void-crack coalescence and void nucleation, and some criteria and models for these effects are discussed. The implications of the finite element results for fracture criteria based on critical stress or strain, or both, is discussed with respect to transition of fracture mode and the angle of initial crack-growth. Localization of flow is discussed as a possible fracture model and as a model for void-crack coalescence.

792 citations

Journal ArticleDOI
TL;DR: In this paper, the J-dominance is used to define the size scale over which large stresses and strains develop while Q scales the near-tip stress distribution and the stress triaxiality achieved ahead of the crack.
Abstract: C entral to the J-based fracture mechanics approach is the concept of J-dominance whereby J alone sets the stress level as well as the size scale of the zone of high stresses and strains. In Part I the idea of a J Q annulus was developed. Within the annulus, the plane strain plastic near-tip fields are members of a family of solutions parameterized by Q when distances are normalized by J σ 0 , where σ0is the yield stress, J and Q have distinct roles: J sets the size scale over which large stresses and strains develop while Q scales the near-tip stress distribution and the stress triaxiality achieved ahead of the crack. Specifically, negative (positive) Q values mean that the hydrostatic stress is reduced (increased) by Qσ0 from the Q = 0 plane strain reference state. Therefore Q provides a quantitative measure of crack-tip constraint, a term widely used in the literature concerning geometry and size effects on a material's resistance to fracture. These developments are discussed further in this paper. It is shown that the J Q approach considerably extends the range of applicability of fracture mechanics for shallow-crack geometries loaded in tension and bending, and deep-crack geometries loaded in tension. The J Q theory provides a framework to organize toughness data as a function of constraint and to utilize such data in engineering applications. Two methods for estimating Q at fully yielded conditions and an interpolation scheme are discussed. The effects of crack size and specimen type on fracture toughness are addressed.

791 citations

References
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Book
01 Jan 1950
TL;DR: In this paper, the solution of two-dimensional non-steady motion problems in two dimensions is studied. But the solution is not a solution to the problem in three dimensions.
Abstract: 1. Introduction 2. Foundations of the thoery 3. General theorems 4. The solution of plastic-elastic problems I 5. The solution of plastic-elastic problems II 6. Plane plastic strain and the theory of the slip-line field 7. Two-dimensional problems of steady motion 8. Non-steady motion problems of steady motion 9. Non-steady motion problems in two dimensions II 10. Axial symmetry 11. Miscellaneous topics 12. Platic anisotropy

7,810 citations

Journal ArticleDOI
James R. Rice1
TL;DR: In this paper, an integral is exhibited which has the same value for all paths surrounding a class of notches in two-dimensional deformation fields of linear or non-linear elastic materials.
Abstract: : An integral is exhibited which has the same value for all paths surrounding a class of notches in two-dimensional deformation fields of linear or non-linear elastic materials. The integral may be evaluated almost by inspection for a few notch configurations. Also, for materials of the elastic- plastic type (treated through a deformation rather than incremental formulation) , with a linear response to small stresses followed by non-linear yielding, the integral may be evaluated in terms of Irwin's stress intensity factor when yielding occurs on a scale small in comparison to notch size. On the other hand, the integral may be expressed in terms of the concentrated deformation field in the vicinity of the notch tip. This implies that some information on strain concentrations is obtainable without recourse to detailed non-linear analyses. Such an approach is exploited here. Applications are made to: Approximate estimates of strain concentrations at smooth ended notch tips in elastic and elastic-plastic materials, A general solution for crack tip separation in the Barenblatt-Dugdale crack model, leading to a proof of the identity of the Griffith theory and Barenblatt cohesive theory for elastic brittle fracture and to the inclusion of strain hardening behavior in the Dugdale model for plane stress yielding, and An approximate perfectly plastic plane strain analysis, based on the slip line theory, of contained plastic deformation at a crack tip and of crack blunting.

7,468 citations

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the C rack-tip strain singularities with the aid of an energy line integral exhibiting path independence for all contours surrounding a crack tip in a two-dimensional deformation field of an elastic material (or elastic/plastic material treated by a deformation theory).
Abstract: C rack-tip strain singularities are investigated with the aid of an energy line integral exhibiting path independence for all contours surrounding a crack tip in a two-dimensional deformation field of an elastic material (or elastic/plastic material treated by a deformation theory). It is argued that the product of stress and strain exhibits a singularity varying inversely with distance from the tip in all materials. Corresponding near crack tip stress and strain fields are obtained for the plane straining of an incompressible elastic/plastic material hardening according to a power law. A noteworthy feature of the solution is the rapid rise of triaxial stress concentration above the flow stress with increasing values of the hardening exponent. Results are presented graphically for a range of hardening exponents, and the interpretation of the solution is aided by a discussion of analogous results in the better understood anti-plane strain case.

2,890 citations

Journal ArticleDOI
TL;DR: In this paper, a total deformation theory of plasticity, in conjunction with two hardening stress-strain relations, is used to determine the dominant singularity at the tip of a crack in a tension field.
Abstract: D istributions of stress occurring at the tip of a crack in a tension field are presented for both plane stress and plane strain. A total deformation theory of plasticity, in conjunction with two hardening stress-strain relations, is used. For applied stress sufficiently low such that the plastic zone is very small relative to the crack length, the dominant singularity can be completely determined with the aid of a path-independent line integral recently given by rice (1967). The amplitude of the tensile stress singularity ahead of the crack is found to be larger in plane strain than in plane stress.

2,667 citations


"On the relationship between critica..." refers background or methods in this paper

  • ...Here, we refer to the asymptotic studies of plane strain crack tip singularities by RICE (196X), RICE and ROSENGREN (1968), and HUTCHINSON (1968), to the subsequent finite element solutions (based on elements which embed the appropriate strain singularity among their admissible deformation fields)…...

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  • ...…strain for (a) small scale yielding (SGC) conditions for non-hardening material from tinite-element computer solution due to OSTERGFWN, and (b) small scale yielding conditions from singularity solution for hardening material due to RICE and ROSENGREN (1968) and HUTCHINSON (1968) (solid lines)....

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  • ...6b) is the singularity solution for a strain-hardening material (n = 0 to 0.2) derived by HUTCHINSON (1968) and RICE and ROSENGREN (1968), again based on the conventional small geometry change (SGC) assumptions....

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