Plane strain deformation near a crack tip in a power-law hardening material
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.
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TL;DR: In this article, a variational principle is established to characterize the flow field in an elastically rigid and incompressible plastic material containing an internal void or voids, and an approximate Rayleigh-Ritz procedure is developed and applied to the enlargement of an isolated spherical void in a nonhardening material.
Abstract: The fracture of ductile solids has frequently been observed to result from the large growth and coalescence of microscopic voids, a process enhanced by the superposition of hydrostatic tensile stresses on a plastic deformation field. The ductile growth of voids is treated here as a problem in continuum plasticity. First, a variational principle is established to characterize the flow field in an elastically rigid and incompressible plastic material containing an internal void or voids, and subjected to a remotely uniform stress and strain rate field. Then an approximate Rayleigh-Ritz procedure is developed and applied to the enlargement of an isolated spherical void in a nonhardening material. Growth is studied in some detail for the case of a remote tensile extension field with superposed hydrostatic stresses. The volume changing contribution to void growth is found to overwhelm the shape changing part when the mean remote normal stress is large, so that growth is essentially spherical. Further, it is found that for any remote strain rate field, the void enlargement rate is amplified over the remote strain rate by a factor rising exponentially with the ratio of mean normal stress to yield stress. Some related results are discussed, including the long cylindrical void considered by F.A. McClintock (1968, J. appl. Mech . 35 , 363), and an approximate relation is given to describe growth of a spherical void in a general remote field. The results suggest a rapidly decreasing fracture ductility with increasing hydrostatic tension.
4,156 citations
TL;DR: This work examined a five-element high-entropy alloy, CrMnFeCoNi, which forms a single-phase face-centered cubic solid solution, and found it to have exceptional damage tolerance with tensile strengths above 1 GPa and fracture toughness values exceeding 200 MPa·m1/2.
Abstract: High-entropy alloys are equiatomic, multi-element systems that can crystallize as a single phase, despite containing multiple elements with different crystal structures. A rationale for this is that the configurational entropy contribution to the total free energy in alloys with five or more major elements may stabilize the solid-solution state relative to multiphase microstructures. We examined a five-element high-entropy alloy, CrMnFeCoNi, which forms a single-phase face-centered cubic solid solution, and found it to have exceptional damage tolerance with tensile strengths above 1 GPa and fracture toughness values exceeding 200 MPa·m(1/2). Furthermore, its mechanical properties actually improve at cryogenic temperatures; we attribute this to a transition from planar-slip dislocation activity at room temperature to deformation by mechanical nanotwinning with decreasing temperature, which results in continuous steady strain hardening.
3,704 citations
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.
1,374 citations
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
TL;DR: In this article, a two-parameter fracture mechanics approach for tensile mode crack tip states in which the fracture toughness and the resistance curve depend on Q, i.e., JC(Q) and JR(Δa, Q), is proposed.
Abstract: Central to the J-based fracture mechanics approach is the existence of a HRR near-tip field which dominates the actual field over size scales comparable to those over which the micro-separation processes are active. There is now general agreement that the applicability of the J-approach is limited to so-called high-constraint crack geometries. We review the J-annulus concept and then develop the idea of a J-Q annulus. Within the J-Q annulus, the full range of high- and low-triaxiality fields are shown to be members of a family of solutions parameterized by Q when distances are measured in terms of J σ 0 , where σ0 is the yield stress. The stress distribution and the maximum stress depend on Q alone while J sets the size scale over which large stresses and strains develop. Full-field solutions show that the Q-family of fields exists near the crack tip of different crack geometries at large-scale yielding. The Q-family provides a framework for quantifying the evolution of constraint as plastic flow progresses from small-scale yielding to fully yielded conditions, and the limiting (steady-state) constraint when it exist. The Q value of a crack geometry can be used to rank its constraint, thus giving a precise meaning to the term crack-tip constraints, a term which is widely used in the fracture literature but has heretofore been unquantified. A two-parameter fracture mechanics approach for tensile mode crack tip states in which the fracture toughness and the resistance curve depend on Q, i. JC(Q) and JR(Δa, Q), is proposed.
1,023 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
TL;DR: In this article, a relation between extent of plastic yielding and external load applied was investigated, and panels containing internal and edge slits were loaded in tension and lengths of plastic zones were measured.
Abstract: Y ielding at the end of a slit in a sheet is investigated, and a relation is obtained between extent of plastic yielding and external load applied. To verify this relation, panels containing internal and edge slits were loaded in tension and lengths of plastic zones were measured.
6,830 citations
TL;DR: In this article, it was shown that at the base of the crack in the direction of its prolongation, the principal stresses are equal, thus tending toward a two-dimensional (two-dimensional) hydrostatic tension.
Abstract: In an earlier paper it was suggested that a knowledge of
the elastic-stress variation in the neighborhood of an
angular corner of an infinite plate would perhaps be of
value in analyzing the stress distribution at the base of a
V-notch. As a part of a more general study, the specific
case of a zero-angle notch, or crack, was carried out to
supplement results obtained by other investigators. This
paper includes remarks upon the antisymmetric, as well
as symmetric, stress distribution, and the circumferential
distribution of distortion strain-energy density. For the
case of a symmetrical loading about the crack, it is shown
that the energy density is not a maximum along the direction
of the crack hut is one third higher at an angle ± cos^(-1)
(1/3); i.e., approximately ±70 deg. It is shown that at the
base of the crack in the direction of its prolongation, the
principal stresses are equal, thus tending toward a state of
(two-dimensional) hydrostatic tension. As the distance
from the point of the crack increases, the distortion strain
energy increases, suggesting the possibility of yielding
ahead of the crack as well as ±70 deg to the sides. The
maximum principal tension stress occurs on ±60 deg rays.
For the antisymmetrical stress distribution the distortion
strain energy is a relative maximum along the crack and
60 per cent lower ± 85 deg to the sides.
2,693 citations
1,330 citations
01 Jan 1965
240 citations