Influence of Cyclic Preloading on the Hydrogen Degradation of Materials

We present the results of numerical analysis of the influence of the mode of preliminary cyclic loading on hydrogen-induced crack growth in high-strength steel with regard for the stress-strain state and diffusion of hydrogen. The elastoplastic stress-strain state at the crack tip under cyclic loading followed by monotonic loading is simulated for the case of high strains. The diffusion of hydrogen at the crack tip is modeled by taking into account the evolution of the stress-strain state from postcyclic compression to tension in the course of hydrogenation. It is shown that the accumulation of hydrogen in the process zone depends on the distribution of residual stresses induced by cyclic preloading.     

Effects of notch radius and anisotropy on the crack tip plastic zone

Factors which influence the shape and size of the plastic zone in the immediate vicinity of a crack tip in isotropic materials at small loads are investigated. The plastic zone dimensions for the opening mode (Mode I) have been calculated over a range of values for the crack tip radius. An increase in tip radius results in an increase in the plastic zone dimension. In anisotropic materials, the orientation of crack slit and the anisotropic yield constants are other factors that affect the plastic zone size and shape. In this paper, typical curves for the shape and size of plastic zone are given to illustrate the influence of normal or shear anisotropic yield constants. For sheet metals the effects of anisotropy on the plastic zone dimensions can be evaluated in terms of R values. Suggested values of constant b for isotropic materials are given if the “radius” approximation is employed for small applied stresses.     

Elastic and plastic stress analysis of an interface crack between two dissimilar layers

In the present paper, the mixed-mode Dugdale model is applied to investigate the plastic zone size and the crack tip opening displacement of an interface crack between two dissimilar layers. In the analysis, both normal and shear stresses are assumed to exist in the plastic zones and satisfy the Von Mises yield criterion. The plastic zone sizes can be determined on condition that the stress intensity factors caused by the stresses in the plastic zones and applied loading are zero. Then, the crack tip opening displacement can be obtained by dislocation theories. In numerical examples, the plane stress condition is considered. The plastic zone size and the crack tip opening displacement of an interface crack between two dissimilar layers under a uniform load are examined. The effects of Dundurs’ parameters and the thickness of materials on the plastic zone size and the crack tip opening displacement are investigated in detail. Numerical results show that in the case of small thickness, the values of the normalized plastic zone size and the normalized crack tip opening displacement decrease with increasing Dundurs’ parameters, α and β, while, in the case of infinite thickness, the value of the normalized plastic zone size is independent of α, and the value is symmetric about the axis on which β = 0.     

An interface crack in a coating-substrate composite with mixed-mode Dugdale corrections

Considering both plane stress and plane strain conditions, the plastic zone size and the crack tip opening displacement of an interface crack between a coating and a semi-infinite substrate under a normal load on the crack surfaces are investigated by the mixed-mode Dugdale model. In the model, stresses applied in the plastic zones satisfy the Von Mises yield criterion. The plastic zone size can be calculated by satisfying the condition that the complex stress intensity factors vanish. After the plastic zone size is solved, the crack tip opening displacement can be obtained by dislocation theories. In numerical examples, a uniform load is considered, and the effects of the normalized elastic modulus (the ratio of the elastic modulus of the coating to the elastic modulus of the substrate) and the normalized crack depth (the ratio of the coating thickness to the interface crack length) on the normalized plastic zone size and the normalized crack tip opening displacement are examined. Numerical examples show in the case of thin coatings, the value of the normalized plastic zone size decreases with increasing the normalized elastic modulus.     

Tensile crack tip fields in elastic-ideally plastic crystals

Crack tip stress and deformation fields are analyzed for tensile-loaded ideally plastic crystals. The specific cases of (0 1 0) cracks growing in the [1 0 1] direction, and (1 0 1) cracks in the [0, 1, 0] direction, are considered for both fcc and bcc crystals which flow according to the critical resolved shear stress criterion. Stationary and quasistatically growing crack fields are considered. The analysis is asymptotic in character; complete elastic-plastic solutions have not been determined. The near-tip stress state is shown to be locally constant within angular sectors that are stressed to yield levels at a stationary crack tip, and to change discontinuously from sector to sector. Near tip deformations are not uniquely determined but fields involving shear displacement discontinuities at sector boundaries are required by the derived stress state. For the growing crack both stress and displacement must be fully continuous near the tip. An asymptotic solution is given that involves angular sectors at the tip that elastically unload from, and then reload to, a plastic state. The associated near-tip velocity field then has discontinuities of slip type at borders of the elastic sectors. The rays, emanating from the crack tip, on which discontinuities occur in the two types of solutions are found to lie either parallel or perpendicular to the family of slip plane traces that are stressed to yield levels by the local stresses. In the latter case the mode of concentrated shear along a ray of discontinuity is of kink type. Some consequences of this are discussed in terms of the dislocation generation and motion necessary to allow the flow predicted macroscopically.     

Development of secondary plastic strips near tensile cracks in the plate

We suggest a method for the solution of the elastoplastic problem of biaxial tension-compression of a thin cracked plate under the assumption that plastic strains at each tip of the crack are localized along three slip lines. The plastic zone is simulated by three inclined slip strips at the tips of the crack. It is assumed that the material of the plate is absolutely elastoplastic and the yield criterion is satisfied along the slip lines. The strips lying on the continuation of the crack are simulated by segments of discontinuity of normal stresses, while the other strips are simulated by segments of discontinuity of tangential stresses Thus, the elastoplastic problem under consideration is reduced to the boundary-value problem of the linear theory of elasticity for a body weakened by branched cuts with unknown lengths and orientations of side branches. These parameters are determined in the process of numerical solution of the problem by the method of singular integral equations. Numerical results are presented for the semiinfinite plane with edge crack and under the conditions of uniform tension at infinity. We present numerical values of some parameters of nonlinear fracture mechanics, such as crack tip opening displacement and lengths and angles of inclination of plastic strips, for various combinations of the components of external load.Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 31, No. 2, pp. 7–13, March – April, 1995.     

Dynamic growth of anti-plane shear cracks in ideally plastic crystals

A near-tip asymptotic analysis is given for the stress and deformation field near the tip of crack propagating dynamically under anti-plane shear in an ideally plastic single crystal. A paricular class of orientations of the crack relative to the crystals is considered so that the yield is so simple diamond shape (relative to directions along perpendicular to the crack) in the plane of the anti-plane shear stresses. The near-tip solution is shown to consists of sectors which carry constant stresses, at yield levels, corresponding to adjacent vertices on the diamond-shaped yield locus, and which are joined along an elastic-plastic shock discontinuity. All plastic flow in the near-tip region occurs in the shock. Plastic strains and particle velocity are finite at the crack tip. The plastic strain is proportional to the elastic strain at onset of yielding and is inversely proportional to the elastic Mach number associated with the speed of crack growth.     

Parameters of deformation mixed modes with account of crack tip curvature

A method for calculating the fields of parameters of the stress-strain state at the crack tip for mixed modes of loading is developed and implemented taking into account the higher-order terms. The influence of the final crack tip curvature radius on the parameters characterizing the mixed failure modes under plane strain is shown. The nature of influence of the mixed modes of loading and the crack geometry on the behavior of dimensionless angular characteristics of the second term in the expansion of the stresses in the plastic crack tip region is established from the calculation results. The relationships between the mixing, constraint and triaxiality parameters are derived in a full range of mixed deformation modes.     

Three-stage model of an elastoplastic cracked body

We propose a three-stage model of an elastoplastic cracked body, which takes into account the evolution of stresses in the prefracture zone according to the complete tensile stress-strain diagram of the investigated material. The zone of loosening corresponding to the last (descending) part of the tensile stressstrain diagram lies in the immediate vicinity of the crack tip. The zone of plastic deformation of the material is located after the zone of loosening. These zones are simulated by separate rectilinear stress-strain diagrams taking into account the effect of linear hardening of the material. Within the framework of the proposed model, we formulate a deformational fracture criterion and determine the characteristics of crack resistance of D16T steel. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 34, No. 1, pp. 59–64, January–February, 1998.     

On the effect of the residual stresses on the crack opening displacement in a cracked sheet

The residual stress and displacement fields caused by localized plastic flow near a mode I crack tip in a sheet under plane stress conditions are investigated. The present study founds on the classical Dugdale scheme of the plastic flow localization. The residual stress field is considered to be induced by reversed plastic flow near the crack tip caused by an unloading. As it is found the residual stresses around the crack compress the crack tip, while the residual tensile stresses in a distant from the crack tip zone occur. It is shown the maximum residual tensile stresses can reach the significant value of the one third of the yield limit. The length of the compressed plastic zone and the residual displacement distributions are obtained. The exact formula for the residual crack opening displacement to estimate the crack closure is found. Then the next loading of the cracked plate is considered. It is shown that the second loading causes the origin of two plastic zones localized near the crack tip and at the point, where the maximum residual tensile stresses are concentrated. Again, according to the Dugdale scheme of the plastic localization, both the plastic flow zones are modelled as narrow stripes on the line extending the crack. To determine three non-dimensional parameters, characterizing the position of the segment-like plastic flow zones, a non-linear system of equations is obtained and analyzed. The exact formula for the crack opening displacement after a loading–unloading cycle is obtained. An asymptotic analysis (as the linear dimension of the distant plastic flow zone compared with the actual crack length is small) is given. It shows that the effect of the distant plastic flow zone appears as some complementary crack closure.     

The influence of aluminium alloy anisotropic texture on crack-tip plasticity

Crack‐tip plasticity in textured aluminium alloys was numerically analysed using an anisotropic yield function and an isotropic hardening law as the material constitutive response. Four real textures obtained from extrusions of rectangular and square shapes as well as five ideal textures typical of rolled products were considered and predicted crack‐tip plastic zones were compared with those obtained using the isotropic von Mises yield criterion. The use of the anisotropic yield function revealed important differences in crack‐tip plasticity compared with the isotropic case. The plastic zone features obtained for different textures were compared to single crystal results published in the open literature and similar crack‐tip plastic strain localization was observed.     

Determining the fracture toughness of metals and alloys under conditions of similarity of local failure

Conclusions The proposed criteria of similarity of local failure make it possible to compare under similar conditions the behavior of metals and alloys at the moment of occurrence of plastic instability at the apex of a crack (defect). It was established that the critical size of the zone of plastic deformation at a defect (crack) with the exceeding of which under the given loading conditions plastic instability occurs is determined by the ratio of the yield strengths of the given material in shear and in tension and depends upon the mechanism of plastic deformation realized at the moment of occurrence of plastic instability.With the use of the criteria of similarity of the constriction of plastic deformation it is fundamentally possible to convert the critical parameters controlling the occurrence of plastic instability at the apex of a crack (defect) under various loading conditions.The results obtained require further analysis and experimental confirmation.Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 13, No. 5, pp. 31–45, September–October, 1977.     

Evaluation of dynamic fracture toughness parameters of locomotive axle steel by instrumented Charpy impact test

The analysis of the energy of fracture of specimens from steel OSL, which is widely used for the manufacture of railway axles under shock loading, is performed. The nature and quantitative parameters of the typical stages of the processes of plastic and brittle fracture, depending on the test temperature and stiffness of the stress state at the tip of the crack‐like defect, are established. It is shown that impact loading at 20 °C leads to the formation of the local zone of plasticity and ductile–brittle fracture of the material. An increased stiffness of the stress state at the tip of the defect at ?40 °C causes brittle fracture. An approach is developed, which is based on using the size of shear lips as a quantitative parameter of fracture under normal and low temperatures, similar in its physical essence to deformation approaches of nonlinear fracture mechanics. Based on this approach and the quantitative analysis of specimen fracture zones, the physical and mechanical scheme of specimen fracture is proposed in the presence of localized plasticity and in its absence near the tip of the concentrator.     

Effects of non-singular stresses on crack-tip fields for pressure-sensitive materials,Part 1: Plane strain case

Mode I near-tip stress fields for elastic perfectly plastic pressure-sensitive materials under plane strain and small-scale yielding conditions are presented. A Coulomb-type yield criterion described by a linear combination of the effective stress and the hydrostatic stress is adopted in the analysis. The finite element computational results sampled at the distance of a few crack opening displacements from the tip show that, as the pressure sensitivity increases, the magnitudes of the normalized radial and hoop stress ahead of the tip decrease, the total angular span of the singular plastic sectors decreases, and the angular span of the elastic sectors bordering the crack surfaces increases. When non-singular T stresses are considered along the boundary layer of the small-scale yielding model, the near-tip stresses decrease as the T stress decreases. The plastic zone shifts toward the crack surfaces as the T stress increases. When the discontinuities of the radial stress and the out-of-plane normal stress along the border between the plastic sector and the elastic sector are allowed, the angular variations of the asymptotic crack-tip fields agree well with those of the finite element computations. Variation of the Q stresses for pressure-sensitive materials can be found from the asymptotic solutions when the plastic zone size ahead of the tip is relatively larger than the crack opening displacement. In addition the T stress is shown to have strong effects on the plastic zone sizes and shapes which could affect the toughening of pressure-sensitive materials.     

Plastic deformation of bcc metal thin foils without dislocation

Heavy plastic deformation of fcc metal thin foils to fracture has been found recently to proceed without involving dislocations, and it results in the formation of high density of vacancy clusters. Thin foil specimens of bcc metals such as V and Mo were plastically deformed to fracture in in situ elongation experiments under an electron microscope. Morphology of thinning and fracture was found to be similar to fcc metals, and no dislocation was observed during heavy deformation. Electron diffraction analysis at the tip of a crack during deformation confirmed a large elastic deformation of up to 5%. Unlike in fcc metal thin foil specimens, point defect clusters were not observed near fractured tips. This difference is attributed to the difference in vacancy reaction, though the deformation in bcc metals without dislocation most likely does produce vacancies.     

An energy balance criterion for crack growth under fatigue loading from considerations of energy of plastic deformation

An approximate analysis using a bilinear representation of the stress-strain behaviour has been made for the energy of plastic deformation at the tip of a crack growing under sinusoidal loading of constant amplitude. The energy of plastic deformation results from hysteretic and non-hysteretic plastic deformation. It is shown that the energy due to hysteresis is independent of the rate of growth of the crack whereas energy due to non-hysteretic plastic deformation is dependent on growth rate. Work hardening due to hysteretic plastic deformation is not considered in the analysis. The energy balance criterion which is basic to fracture mechanics has been applied to the problem of crack growth under cyclic loading, considering the energy due to hysteretic plastic deformation in the plastic enclave as obtained in the analysis. The equation of energy balance results in an expression for crack growth rate, consistent with the general trends observed in experiments. Some of the merits and limitations of the energy formulation of fatigue crack growth have been discussed.     

Stress-Strain State and Energy Fluxes in a Plate Containing a Stationary Crack under Impulsive Loading

We study the stress-strain state and energy fluxes in a continuous infinite plate and in a plate containing a stationary crack of finite length under impulsive loading. For this purpose, we develop a model of formation of the zone of elevated stresses and the zone of unloading as well as a numerical procedure for the evaluation of their parameters. We deduce analytic expressions for the quantitative analysis of the stress-strain state and energy fluxes in the plate near the tip of the stationary crack under arbitrary impulsive loading. The theoretical results are compared with the experimental data on the initiation of main cracks in plane specimens made of solid polymers. We formulate a quantitative criterion for the difference between the dynamic and quasistatic loading of a crack and show that the dynamic and static fracture processes can be described within the framework of a single approach.     

Failure prediction in toughened epoxy resins

In order to improve the damage tolerance of composites and the performance of adhesives, one of the methods being considered is toughened or modified epoxy resins. The modifiers which are commonly used are CTBN rubber and inorganic fillers. A major toughening mechanism causing the increased toughness is the shear deformation process occurring near the crack tip. The effect of such a deformation process is to blunt the crack tip and increase the size of the plastic zone. Several models are available to predict the toughness on the basis of plastic zone size, crack tip opening displacement or crack tip radius, but these are only applicable to Mode I crack extension. Also, most of these approaches use only one stress component which is normal to the crack plane to predict the fracture toughness. The present paper reviews the existing models and suggests a criterion based on the phenomenological approach to failure in order to study the yielding and fracture toughness behavior of both unmodified and modified epoxies. The proposed yield and fracture criteria give predictions in good agreement with experimental results.     

BASIC DIAGRAMS OF CYCLIC CRACK GROWTH RESISTANCE OF TITANIUM ALLOYS

Abstract— Basic diagrams of the cyclic crack growth resistance of two of the most investigated titanium alloys, namely Ti-6A1–4V and Ti-6A1–6V-2Sn, are presented. Diagrams are plotted for, in-air, distilled water and 3.5% NaCl solution, which are necessary for lifetime calculations of structural elements made of these metals. The dependency of cyclic crack growth resistance on the yield strength is established. It is shown that cyclic crack growth resistance of titanium alloys in corrosive environments is determined not only by the stress-strain state but also by the electrochemical conditions at the corrosion fatigue crack tip, which for aqueous environments can be characterized integrally by the hydrogen index of the environment and the electrode potential of the metal. Therefore, cyclic corrosion crack growth resistance testing should be performed under constant electrochemical conditions at the corrosion fatigue crack tip or these conditions should be taken into account. A new method of plotting the basic cyclic corrosion crack growth resistance diagrams of titanium alloys is considered.     

Generalized griffith problem of shear with regard for the roughness of the crack surfaces

We study the generalized Griffith problem of longitudinal and transverse shear with regard for the roughness of the crack surfaces. The crack lips are modeled in the form of teeth. We study the process of contact of the teeth and its influence on the stress-strain state at the crack tip. The prefracture zone is modeled by cuts whose lips are in the complex stressed state and, hence, suffer the action of average shear and tensile stresses satisfying the Huber-Mises relations. As a result, we obtain expressions for the length of the plastic zone and crack-tip displacements in the cases of both transverse and longitudinal shear. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 36, No. 2, pp. 49–54, March-April, 2000.