Physical models for cleavage fracture at various temperatures—Bases for local approach to fracture of HSLA steel

The author proposes the critical events controlling cleavage at various temperatures: at a very low temperature (−196 °C), critical event is the nucleation of a crack in ferrite at the precrack tip. At a moderate low temperature (around −100 °C), the critical event is the propagation of a carbide crack into the ferrite grain. With increasing temperature (around DBTT −80 °C), the carbide crack eligible to propagate into the ferrite grain should be the one initiated by a critical strain higher than that to initiate a carbide crack at low temperatures. The higher critical strain increases the flow stress by work hardening for making up the effect of lowering yield stress. At a higher temperature (−30 °C) after the crack tip is blunted to more than 60 μm and a fibrous crack extends, the critical event for cleavage fracture is the propagation of a grain-sized crack.     

Shear loaded interface crack under the influence of friction: a finite difference solution

Formulation of the elastic two‐dimensional problem of contact with friction is presented. Two‐dimensional equilibrium equations and boundary conditions in an orthogonal curvilinear co‐ordinate system are written explicitly. The above formulation is solved with the aid of the finite difference technique. An iterative algorithm which does not require load increments is employed for solving interface fracture problems with contact and friction subjected to a monotonically increasing load. The J‐integral is extended for problems in which there is friction along the crack faces. Stress intensity factors are calculated by means of the J‐integral, as well as an asymptotic expansion of the tangential shift. Two problems are analysed: (1) a crack in homogeneous material in the presence of friction involving stationary contact; and (2) an interface crack in the presence of friction involving receding contact. Results are compared to those found by analytical and semi‐analytical methods which are presented in the literature, as well as to those obtained by means of the finite element method. The accuracy of the results establishes the reliability of the finite difference analysis, as well as the post‐processors. In addition, a problem involving stick conditions is considered. It is observed that with increasing friction, the normal gaps and tangential shifts decrease. The size of the contact zone increases and values of the stress intensity factor decrease. Copyright © 2004 John Wiley & Sons, Ltd.     

Fatigue of V-notched members: Short crack behavior and endurance limit

A previous experimental investigation showed that the short crack behavior in severe V-notched geometries is essentially characterized by an initial transient variation of the crack opening level within the notch plastic zone. This result is exploited to derive a general formulation of the endurance limit of V-notched members. Analytical solutions for the stress intensity factor and the notch plastic zone extent are obtained to compute the effective crack driving force ΔK_eff as a function of notch geometry, crack length and nominal stress. Then, the endurance limit is determined as the nominal stress below which an initiated crack becomes non-propagating, i.e. by equating the minimum ΔK_eff value at the end of the plastic zone to a threshold value. By using Irwin's redistribution principle which allows us to make relations between the V-notch elastic and plastic fields, the following results are obtained. The endurance limit can be computed only from the V-notch “stress intensity factor” and the material threshold and cyclic yield stress. The endurance limit dependence on the threshold diminishes as the notch angle increases from zero and vanishes in the limit case of a smooth surface. When the notch contains a pre-existing crack, a Kitagawa-type endurance diagram is obtained. The uncracked notch endurance limit, the critical crack length and the slope of the decrease beyond this length, increase with increasing notch angle, and there is a total coincidence with the Kitagawa diagram in the limit case where the notch angle tends to 180°. This result shows that a global theory should govern at one and the same time the short crack behavior in smooth and severe geometries.     

A fatigue crack propagation model for strain hardening materials

In this paper a crack propagation model based on Tomkins concept (dl/dN ∝ Δε_p · ω) has been developed using the theoretically developed cyclic plastic zone sizes. The crack propagation rates are found to be functions of stress intensity factor, Elber's effective stress range ratio, cyclic yield strength of material, crack length, specimen width and cyclic strain hardening exponent. Suitably grouped to give the crack growth rate in terms of five constants termed as Loading Constant, Material constant, Crack size constant, specimen Width Constant and Stress Intensity Exponent. The crack growth rates found by theory are compared with the experimental results available in literature and a good agreement is found.     

Fracture mechanics analysis of asperity cracking due to adhesive normal contact

A two-dimensional linear-elastic fracture mechanics analysis of asperity cracking induced by adhesive normal contact was performed with the finite element method. Normal contact between two elastic asperities was analyzed with the equivalent contact system of an elastic asperity with equivalent radius of curvature and effective elastic modulus compressed by a rigid plane. Surface adhesion was modeled by nonlinear springs obeying a constitutive force-distance law derived from the Lennard–Jones potential. The maximum ranges of the tensile and shear stress intensity factors were used to determine the crack-growth direction and the dominant mode of asperity fracture in terms of the Maugis parameter (a function of the equivalent radius of curvature, work of adhesion, effective elastic modulus, and intermolecular equilibrium distance), friction coefficient at the crack interface, maximum surface interference, and crack position. Finite element simulation results indicate that the direction and the rate of crack growth are mostly affected by the Maugis parameter and the maximum surface interference. A transition from shear to tensile dominant mode of crack growth is encountered with the increase of the Maugis parameter and/or the decrease of the maximum surface interference. Opening, slip, and stick between the crack faces during loading and unloading are discussed in the context of crack mechanism maps.     

Growth mechanism of stress corrosion cracking in high strength steel

Stress corrosion crack growth rates are measured at sveral stress intensity levels for low-tempered 4340 steel in 0.1N H₂SO₄ solution. The characteristics of the growth rates are divided into three regions of stress intensity factors: Region I near K_1SCC; Region III near unstable fracture toughness, K_1SC; and Region II, which lies between the two. K_1SCC is the value of K at which no crack growth can be detected after 240 hr.

In order to explain these experimental results, the crack initiation analysis reported in a previous paper is extended to the growth rates. A detached crack initiates and grows at the tip of an already existing crack. When the detached crack reaches the tip of the main crack, the process repeats as a new existing crack.

A relationship between crack growth rate, v, and stress intensity factor, K, is obtained as a function of b/a and a = b + d, where b is the distance from the tip of the main crack to the detached crack, and d is the ydrogen atom saturated domain.

The experimental data are in good agreement with the theoretical values in Region II when a = 0.02 mm, b/a = 0.8, c₁/c₀ = 2.8 for 200°C tempered specimens and a = 0.015 mm, b/a = 0.7, c₁/c₀ = 3.0, ρ_b = 0.055 mm for 400°C tempered specimens, where ρ_b is a fictitious notch radius. The plateau part in Region II for 400°C tempered specimens is also successfully explained by the present theory. For Region III, the value of b/a will be almost equal to 1 because v → ∞ for b/a → 1. On the other hand, for Region I, b/a will be zero, since the value of v becomes negligibly small and no crack growth is observable.     

Interlaminar fatigue crack growth of cross-ply composites under thermal cycles

The fatigue growth of a fiber reinforced composite laminate was characterized under thermal cycling using a combined experimental and computational investigation. Twenty-four ply composite laminates ([0°₁₂/90°₁₂]) are fabricated with a pre-existing delamination, and subjected to thermal cycling in an environmental chamber. The large mismatch in the coefficients of thermal expansion is used to grow an interlaminar crack at the interface of the 0° and 90° laminae. This thermal fatigue crack growth behavior is investigated for different amplitudes of temperature change (ΔT = 30–140 °C). The inspection of fracture surfaces, after completion of the fatigue tests, reveals an angled or kinked crack front growth with greater propagation distances near the free-surfaces/edges. Due to the non-uniform crack growth across the specimen thickness, three-dimensional finite element analyses are performed to investigate the fatigue growth mechanisms under thermal load. From the analysis, the energy release rate as well as the mixed-mode stress intensity factors is calculated and the variations of these fracture parameters are found to be consistent with the observed crack front configuration. Using the computed results, the experimentally measured crack growth rates are also correlated with the amplitude of energy release rate, and a power law form of the fatigue law is established. The relevant coefficients as well as the threshold energy release rate are also determined. The present analysis is useful for not only understanding the fatigue delamination mechanisms under thermal cycling but also for estimating the threshold temperature variation that is needed to drive crack growth.     

Mode II stress intensity factors for central slant cracks with frictional surfaces in uniaxially compressed plates

The effect of crack surface friction on mode II stress intensity factor (SIF) of a central slant crack in a plate uniformly loaded in uniaxial compression is quantified. A previously developed two-dimensional finite element analysis was utilised after its modification to accommodate the friction between the crack surfaces. The plane strain state was assumed. A new numerical technique was devised to avoid the iteration procedures, which had to be employed due to the existence of frictional forces.

The crack inclination angle varied between zero and 75° measured from the horizontal direction. The coefficient of friction of the crack surfaces changed from zero to 1. In case of relatively sliding crack surfaces, mode II SIF existed. As is well known, the resulting mode II SIF decreased with increasing the coefficient of friction of the crack surfaces. Further, mode II SIF increased with increasing crack line inclination angle and then decreased after reaching a maximum value. The angle corresponding to that maximum SIF increased as the coefficient of friction of the crack surfaces increased.     

Pressure with friction of a perfectly rigid die upon an elastic half space with cracks

We study the interaction of a rigid die with a base of any shape and the surface of an elastic half space containing cracks in the presence of friction in the contact zone. The solution of the plane contact problem of the theory of elasticity is obtained by the method of singular integral equations. The detailed analysis of the problem is performed for the case where the base of the die is parabolic and a crack is rectilinear and appears on the surface of half space. We also investigate the effects of the friction coefficient, crack length, its orientation, and location on stress intensity factors KI and KII at the crack tip and the distribution of contact stresses under the die.     

Fatigue crack-growth characteristics of two magnesium alloys

Magnesium alloys are being increasingly used for engineering applications. Fatigue crack-growth data have therefore been obtained for a high strength magnesium-Zr alloy and a medium strength, weldable magnesium-Mn alloy. The results of tests on sheet material are presented in terms of the range of stress intensity factor ΔK. Critical values of ΔK necessary for fatigue crack growth ΔK_c were also obtained. The behaviour of the two alloys was similar; both rates of crack growth and ΔK_c were sensitive to mean stress. Fatigue crack growth was entirely on a 90° plane with no sign of the transition to crack growth or 45° planes usually observed in sheet materials. This was ascribed to the effects of preferred orientation of the crystal structure.     

Finite element analysis of magnetic disk with a horizontal subsurface crack

Sliding contact of a rigid rough surface with a semi‐infinite medium including a horizontal subsurface crack was investigated by using linear elastic fracture mechanics and finite element method (FEM). The fractal geometry was used to characterize the rigid rough surface. The propagation of crack was studied with the shear and tensile stress intensity factors. The effect of surface roughness, crack length to depth ratio and friction at the contact and crack interfaces was investigated by using the FEM. It was shown that increasing friction coefficient at the contact interface increases both K_II and K_I.     

The effect of hold-time on fatigue crack growth behaviors of WASPALOY alloy at elevated temperature

The effect of hold-time on fatigue crack growth behaviors of WASPALOY alloy was investigated. It was found that the role of hold-time depends on the competition between the harmful environmental effect and the beneficial effect of creep. If temperature is not higher than 705 °C, fatigue crack growth rate of WASPALOY alloy increases with hold-time. On the contrary, hold-time plays a beneficial role on steady state fatigue crack growth of WASPALOY alloy at 760 °C and lower stress intensity factor. The beneficial effect of hold-time was attributed to the creep caused stress relaxation during the hold-time. However, accumulated creep damages cause to cavity nucleation and growth at the grain boundaries, and then accelerate fatigue crack growth. Hold-time plays a harmful role during the final stage of fatigue crack growth.     

Plane Problem of a Crack on the Interface of Orthotropic Plates with Friction of Crack Lips

We consider a plane problem of a crack on the interface of different orthotropic arbitrarily oriented semiinfinite spaces subjected to the action of uniform tensile and shear forces applied at infinity. In the vicinity of the crack tip, the crack lips smoothly close up to form a contact zone of a priori unknown length in the presence of constant friction between the lips. A transcendental equation for the length of the contact zone is deduced and analyzed. As a result, we obtain the dependences of the relative length of the contact zone and the stress intensity factors on the orientation of the principal directions of orthotropy for different values of the external load and boundary friction.     

Partial closure and frictional slip of 3-D cracks

The effects of partial closure and frictional slip of three-dimensional cracks on the stress intensity factors are studied using the eigenstrain method. The formulation, based on the correct modelling of the boundary conditions on the crack faces, is presented separately for partial closure and frictional slip, and applied to two simpler cases: partial closure of a surface-breaking crack normal to the free surface and under a residual stress field; and frictional slip of a completely closed crack under normal and shear tractions. The evolution of crack closure with the increase of crack depth and its influence on the stress intensity factor are examined and compared with a simple model for the first problem. the effect of coefficient of friction between crack faces on the stress intensity factors is investigated for the second problem.     

The (cleavage) strength of pre-cracked polycrystals

The fracture mechanics stress intensity, K, measured for the cleavage strength of carbon steel by Professor Yokobori and colleagues, at Tohoku University and elsewhere, is shown to follow a Hall-Petch dependence on average grain diameter, l, in accordance with the model-based relationship K = c's^1/2[σ₀+kl^−1/2]; for which c' is a numerical factor, 5 is the effective length of the local plastic zone associated with unstable crack growth, σ₀ is a friction stress for appropriate dislocation movement within the polycrystal grains and k is a microstructural stress intensity intermediate between that for the plastic flow or fracture of crack-free material. The separated terms in the K relationship are matched with corresponding Hall-Petch friction stress and microstructural stress intensity measurements for yielding and fracture. In this way, the K relationship is proposed to provide a bridge for the goal set some time ago by Professor Yokobori of combining the microscopic and macroscopic (continuum) viewpoints for understanding the fracture strength properties of engineering materials.     

Fracture behavior of 9% nickel high-strength steel at various temperatures: Part I. Tensile tests

Fracture behavior of a 9% nickel 1000 MPa grade high-strength steel was investigated with tensile tests at various temperatures. Four critical stresses were found, which determined the fracture behaviors at various temperatures. Various fracture behaviors could be classified into three categories: (1) at −196 °C, a longitudinal crack initiated from the center of the necking region and propagated along the tensile direction to the regions close to both ends of the necking, it then changed the orientation and developed into two transverse cracks which propagated into opposite directions on two separated cross-sections. (2) In the range of −30 °C to 20 °C, the fracture surfaces were composed of typical center-fibrous-initiation region, middle shear-radical region and outer shear-lip region. (3) In the range of −150 °C to −60 °C, the middle shear-radiation region showed a very rough pattern with several convex ridges. Fracture mechanisms were analyzed by combining various fracture morphologies with FEM-calculated results of stress and strain.     

裂纹面动摩擦作用对脆性材料动力破坏的影响EI北大核心CSCD

基于岩石类材料的I型裂纹模型,提出了一种考虑裂纹密度、裂纹相互作用以及裂纹面动摩擦作用的脆性材料动力模型。以正方形阵列分布的裂纹为例,定量分析了不同裂纹密度及不同摩擦行为对试件的裂纹扩展过程、试件受力和破坏的影响。数值计算结果表明:随着裂纹密度增大,裂纹间的相互作用增强,试件破坏时的加载应力降低,惯性效应引起试件轴向附加应力增大。裂纹面的滑动会降低裂纹面的动摩擦系数,促进裂纹发展,并降低试件的强度。相对于常数摩擦系数,考虑速度及状态依赖型摩擦模型对裂纹面的滑动过程更为合理。动强度因子对比结果显示出试件明显的应变率效应和尺寸效应。     

Stress intensity factors of a central slant crack with frictional surfaces in plates with biaxial loading

The stress intensity factor is a traditional topic in mechanics and there have been many solutions for many different cases. The closed frictional crack problem has been modeled in the rock mechanics field where fractures are mostly under compression. Further, the effect of finite plate dimensions under biaxial loading has not been considered in the literature. The key contribution of the present paper is to evaluate the effect of the crack length to plate width ratio on the mode I and II stress intensity factors (SIF) of a central slant crack with frictional surfaces in plates with biaxial loading of different patterns, i.e. tension-tension, tension-compression, compression-tension or compression-compression. A plane strain elastic two-dimensional finite element analysis was adopted. Crack length to plate width ratios equal to 0.1, 0.3 and 0.5 with biaxial ratios from –1 to 1, crack angles from 0° to 90° and friction coefficients from 0 to 1 were considered. Contact regimes and the effect of the crack length to plate width ratio were found dependent on biaxial ratio and pattern, friction coefficient and crack angle.     

On the photoelastic determination of complex stress intensity factors

An improvement of the one-parameter extrapolation method of photoelastic determination of complex (mixed-mode) stress intensity factors at straight or curvilinear crack tips in a plane isotropic elastic medium due to Smith et al. [12, 13] can be achieved by measuring the absolute value of such a factor on the isochromatic fringes along properly selected polar directions and not at the maxima of the isochromatic fringes. In this way, the unknown value of the constant term of the stress field near the crack tip is taken into account. It is seen that it is always possible to find at least one appropriate polar direction to measure the absolute value of the stress intensity factor. In the case of Mode I stress intensity factors, these polar angles are = ± 120° and not = ± 90° as generally considered previously. Some numerical results are also presented in this special case and show the efficiency of the present method.     

Stress intensity factors in a cracked infinite elastic wedge loaded by a rigid punch

The paper considers splitting a plane elastic wedge-shaped solid through the application of a rigid punch. It is assumed that the coefficient of friction on the contact area is constant, the problem has a plane of symmetry with respect to loading and geometry, and the crack lies in the plane of symmetry. The problem is formulated in terms of a system of integral equations with the contact stress and the derivative of the crack surface displacement as the unknown functions. The solution is obtained for an internal crack and for an edge crack. The results include primarily the stress intensity factors at the crack tips, and the measure of the stress singularity at the wedge apex, and at the end points of the contact area.