Subcritical crack growth in strain-hardening materials with allowance for strain anisotropy

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 24, No. 2, pp. 90–94, February, 1988.     

Mixed mode fatigue crack growth and the strain energy density factor

The strain energy density factor S was first proposed by Sih for the prediction of the critical of the load and failure direction under monotonic, mixed mode loading condition. It seems a natural extension to apply the same concept to fatigue crack propagation. However, a close examination of the existing theory indicates that the Strain Energy Density Factor cannot logically account for the phenomena of the R-ratio effect and crack arrest. Thus, modification is necessary before the concept can be applied successfully for the prediction of mixed mode fatigue crack propagation.Based on the concept of hysteresis energy dissipation, an effective strain energy density factor range, ΔS_p,eff, is proposed for the correlation of fatigue crack growth data. ΔS_p,eff is consistent with the concept of crack closure. Experimental investigation indicates that it could predict the crack growth rates and trajectories.     

Fatigue crack growth under anti-plane shear mode deformation

In this paper, the theory of the steady growth of fatigue crack in an infinite medium under the periodic anti-plane remote shear loading has been examined. The criterion of accumulative plastic work for material failure associated with the slip displacement in the fracture process zone of Dugdale type ahead of the crack tip is employed in the analysis. The effect of the locked dislocation in the fracture process zone is considered. Under the assumption that the speed of fatigue crack propagation remains uniform through the fracture process zone, the steady speed of fatigue crack can be expressed as a function of the range of the applied shearing stress and the maximum shearing stress. The effect of the crack size on the fatigue crack speed is discussed. The effect of the finite width of specimen on the speed of fatigue crack speed is investigated. The differences between the present work and the previous studies on fatigue crack speed are discussed.     

Damage accumulation for growth of anti-plane crack in work-hardening material

Elastic–plastic solutions of an anti-plane crack in an infinite body are used in conjunction with a continuum damage model to describe the conditions necessary for the onset of crack instability, fatigue crack propagation due to cyclic loading, and rates of crack growth due to time dependent events. A power law relates the stress to the strain of the material. The damage, which invokes nucleation, growth and coalescence of microvoids due to elevated strain, is confined to the plastic zone surrounding the crack tip. For applied loading below the yield stress, the small-scale and large-scale yielding solutions are used to determine the influence of strain hardening on crack instability and failure. Crack growth due to cyclic loading and time-dependent deformations are studied using the small-scale yielding solution of the deformation theory of plasticity.     

Elastic-plastic mechanics of steady crack growth under anti-plane shear

For a crack with steady growth under anti-plane shear, analysis shows a primary plastic zone included in an angle of ±19.7° ahead of the crack tip, and two very thin secondary (reverse) plastic zones along the crack flanks, each included in an angle of 0.37°. Numerical solutions give the shape of the plastic zones which determine the active and residual plastic strains, and give the crack tip displacement, which is approximately 0.07 of that for monotonic loading without growth. The length of the primary plastic zone is almost the same as that without growth, but the thickness is about 3/5 as great. Coupled with ductile fracture criteria, the present results predict initially stable crack growth, whereas analyses based on the simplification of yielding on just one plane predict unstable fracture immediately following initiation.     

Local crack tip strain behavior during fatigue crack initiation and propagation in polycarbonate

To investigate whether the two fatigue processes of crack initiation and propagation can be combined, the change of local notch root strain and its history, as well as the change of local crack tip strain and the local strain history, of a fatigued element ahead of the propagating crack tip up to failure in a polycarbonate subjected to low-cycle fatigue tests are measured by the fine grid method. As a result, the existence of a unified local strain field in which the two fatigue processes can be substantially combined is experimentally confirmed. Therefore, the local crack tip strain may be examined by a simpler, one-parameter approach for fatigue life estimation.     

Anisotropic plastic stress field at a mixed-mode crack tip under plane and anti-plane strain

On condition that any perfectly plastic stress component at a crack tip is nothingbut the function ofθ.by making use of equilibrium equations,anisotropic plastic stress-strain-rate relations,compatibility equations and Hill anisotropic plastic yieldcondition,in the present paper,we derive the generally analytical expressions of theanisotropic plastic stress field at a mixed-mode crack tip under plane and anti-planestrain.Applying these generally analytical expressions to the mixed-mode cracks,wecan obtain the analytical expressions of anisotropic plastic stress fields at the tips ofmixed-modeⅠ-Ⅲ,Ⅱ-ⅢandⅠ-Ⅱ-Ⅲcracks.     

On perfectly stress field at a mixed-mode crack tip under plane and anti-plane strain

In [1], under the condition that all the perfectly plastic stress components at a crack tip are functions of ϕ only, making use of equilibrium equations, stress-strain rate relations, compatibility equations and yield condition. Lin derived the general analytical expressions of the perfectly plastic stress field at a mixed-mode crack tip under plane and anti-plane strain. But in [1] there were several restrictions on the proportionality factor γ in the stress-strain rate relations, such as supposing that γ is independent of ϕ and supposing that γ=c or cr⁻¹. In this paper, we abolish these restrictions. The cases in [1], γ=cr^d (n=0 or-1) are the special cases of this paper.     

Electric-field-induced fatigue crack growth in ferroelectric ceramics

Electric-field-induced fatigue crack growth in pre-cracked PZT ferroelectric ceramics is experimentally investigated in this work. It is found that the crack open and close under an alternating electric field is a major mechanism of crack propagation. The experimental results also show that the frequency, waveform, as well as the amplitude ratio, of the electric loading, play important roles in electric-field-induced fatigue cracking. Empirical formulations of fatigue crack propagation rates are obtained based on the experimental results. It is revealed that the crack grows at a nearly constant rate when the loading frequency is below 100 Hz. However, with the increase of the loading frequency over 125 Hz, the crack propagation rate diminishes rapidly.     

One model of fatigue crack growth

A model for crack growth is proposed based on studies of the variation in the curvature radius at the crack tip during cyclic loading. Relations are obtained between mechanical material characteristics, crack geometry, and the rate of crack growth in a structure under cyclic loading. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 167–175, July–August, 2009.     

Subcritical crack growth in an aging plate with variable elastic modulus

The paper addresses subcritical growth of a crack in a thin isotropic plate made of an aging viscoelastic material with time-dependent elastic modulus. The behavior of the material is described by Arutyunyan’s creep theory. To simulate fracture, a modified Leonov–Panasyuk–Dugdale model and a critical crack opening displacement criterion are used. An equation describing the subcritical growth of the crack is derived assuming that Poisson’s ratio is constant. As an example, the critical loads are determined, and curves of subcritical crack growth are plotted for a specific material. The results are compared with the case of constant elastic modulus     

Quasi-static growth and dynamic extension of anti-plane shear crack in periodically nonhomogenous elastic material

The quasi-static growth of an anti-plane shear crack in a periodically nonhomogeneous elastic material is considered. An effective velocity dependent energy release rate is found for a semi-infinite crack. Approximate expressions of stress intensity factors for in-plane cracks in periodically nonhomogeneous material are also given.     

Subcritical growth of high-cycle fatigue cracks in finite thin isotropic plates

The problem of constructing a two-stage model of the motion of a fatigue crack in finite thin isotropic plates under symmetric tension-compression is formulated, and a method for its solution is considered. The two-stage nature is regarded as the presence of the incubation and propagation stages. The model is constructed by jointly considering the resolving equations of the theory of elasticity and the evolutionary equations of the mechanics of continuous damage. The damage function's attaining the critical value is considered as a criterion of initiation of local fracture and movement of a fatigue crack. Plates containing central and lateral cracks are considered. The effect of the level of stresses, the finiteness of the plate, the initial length of the crack, and the behavior of the length of the plastic zone on fracture kinetics is evaluated. The present work was carried out with financial support from the European Community in accordance with the INTAS-UA 95-0202 International Project. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 7, pp. 106–116, July, 2000.     

Subcritical crack growth in weak interface under mixed mode in two dimension

Constitutive equations, which govern subcritical crack growth within a weak brittle interface, are derived assuming mixed-mode loading, i.e., both tensile and shear stresses acting at the crack tip. The subcritical crack growth is assumed to be caused by the classical activation mechanism of fluctuation fracture kinetics. To derive the constitutive equations, two approaches are developed. The first approach is process-zone-detail-independent (PZI), which ignores any details of the process zone, i.e., a near-crack-tip zone of significant damage resulting in fracture, and takes into account only the process zone length. The second approach is process-zone-detail-dependent (PZD), which takes into account some details of the process-zone structure. After some general considerations including 3D case, the detailed consideration is given for 2D case, particularly, for plane strain. Illustrative calculated examples of the obtained theoretical results are presented.     

Intergranular strain evolution near fatigue crack tips in polycrystalline metals

The deformation field near a steady fatigue crack includes a plastic zone in front of the crack tip and a plastic wake behind it, and the magnitude, distribution, and history of the residual strain along the crack path depend on the stress multiaxiality, material properties, and history of stress intensity factor and crack growth rate. An in situ, full-field, non-destructive measurement of lattice strain (which relies on the intergranular interactions of the inhomogeneous deformation fields in neighboring grains) by neutron diffraction techniques has been performed for the fatigue test of a Ni-based superalloy compact tension specimen. These microscopic grain level measurements provided unprecedented information on the fatigue growth mechanisms. A two-scale model is developed to predict the lattice strain evolution near fatigue crack tips in polycrystalline materials. An irreversible, hysteretic cohesive interface model is adopted to simulate a steady fatigue crack, which allows us to generate the stress/strain distribution and history near the fatigue crack tip. The continuum deformation history is used as inputs for the micromechanical analysis of lattice strain evolution using the slip-based crystal plasticity model, thus making a mechanistic connection between macro- and micro-strains. Predictions from perfect grain-boundary simulations exhibit the same lattice strain distributions as in neutron diffraction measurements, except for discrepancies near the crack tip within about one-tenth of the plastic zone size. By considering the intergranular damage, which leads to vanishing intergranular strains as damage proceeds, we find a significantly improved agreement between predicted and measured lattice strains inside the fatigue process zone. Consequently, the intergranular damage near fatigue crack tip is concluded to be responsible for fatigue crack growth.     

Three-dimensional transverse fatigue crack growth in rail head

Results are given in terms of crack growth area and tonnage of train load. A three-dimensional finite element procedure is developed for analyzing multiple-mode transverse fatigue crack growth in a rail section. Stress and failure analysis are performed for each increment of non-self-similar crack growth up to the point of global instability that is assumed to be governed by the fracture toughness of the rail steel. The strain energy density criterion is adopted to predict the crack profiles developed from a two-stage fatigue loading cycle where both Mode I and III crack extension are present. Use is made of the material data obtained from the past and present TSC programs for predicting the remaining life of a 132 lb/ft rail head with an initial transverse circular crack of 0.50 in. in diameter. The number of cycles to failure are estimated for four different vertical load and initial crack positions.