The specific enthalpy of fracture for beta Ti-15-3 alloy

Fatigue crack propagation (FCP) experiments were conducted on beta Ti-15-3 alloy under various loading conditions to examine the constancy of the specific enthalpy for fracture, advanced by the Crack Layer (CL) theory as a material parameter characteristic of its intrinsic toughness. The energy release rate and the irreversible work were determined from load-displacement curves during crack propagation. Microscopic and diffraction analyses were conducted to identify the damage mechanisms ahead of the crack tip. A damage zone whose geometry exhibited plane strain character at the initial stage of crack propagation was observed optically. The damage zone transformed into plane stress configuration when the crack reached half its critical length. Damage mechanisms involved slip lines and microcracking which is believed to ensue from intense accumulation of slip processes. The magnitude of microcracking became more weighty as the crack moved deeper into plane stress dominance. The damage preceding crack advance was quantitatively assessed as the crack resistance moment which is the volume of transformed material per unit crack extension. Application of the CL theory to the data generated under a wide range of applied stress levels gave rise to a constant value of the specific enthalpy of fracture, 20 MJ/m³. This value is in close agreement with the specific energy of slip lines computed from microstructural considerations.     

The cohesive zone model in a problem of delayed hydride cracking of zirconium alloys

The crack tip model with the cohesive zone ahead of a finite crack tip has been presented. The estimation of the length of the cohesive zone and the crack tip opening displacement is based on the comparison of the local stress concentration, according to Westergaard's theory, with the cohesive stress. To calculate the cohesive stress, von Mises yield condition at the boundary of the cohesive zone is employed for plane strain and plane stress. The model of the stress distribution with the maximum stress within the cohesive zone is discussed. Local criterion of brittle fracture and modelling of the fracture process zone by cohesive zone were used to describe fracture initiation at the hydride platelet in the process zone ahead of the crack tip. It was shown that the theoretical K _IH-estimation applied to the case of mixed plane condition within the process zone is qualitatively consistent with experimental data for unirradiated Zr-2.5Nb alloy. In the framework of the proposed model, the theoretical value of K ^H _IC for a single hydride platelet at the crack tip has been also estimated.     

The cohesive zone model in a problem of delayed hydride cracking of zirconium alloys

The crack tip model with the cohesive zone ahead of a finite crack tip has been presented. The estimation of the length of the cohesive zone and the crack tip opening displacement is based on the comparison of the local stress concentration, according to Westergaard's theory, with the cohesive stress. To calculate the cohesive stress, von Mises yield condition at the boundary of the cohesive zone is employed for plane strain and plane stress. The model of the stress distribution with the maximum stress within the cohesive zone is discussed. Local criterion of brittle fracture and modelling of the fracture process zone by cohesive zone were used to describe fracture initiation at the hydride platelet in the process zone ahead of the crack tip. It was shown that the theoretical K _IH-estimation applied to the case of mixed plane condition within the process zone is qualitatively consistent with experimental data for unirradiated Zr-2.5Nb alloy. In the framework of the proposed model, the theoretical value of K ^H _IC for a single hydride platelet at the crack tip has been also estimated.     

Application of the double slip plane crack model to temperature and strain rate sensitive BCC metals

The double slip plane crack model proposed by Weertman, Lin and Thomson (1982) has been applied to model the effect of temperature and strain rate on the stress intensity factor at a crack tip in temperature and strain rate sensitive materials. Increase in temperature or decrease in strain rate (as well as a decrease in slip plane spacing) are shown to increase the shielding of the crack tip by dislocation distributions on the slip planes. Furthermore, the effect of temperature on the fracture toughness, K_llc, at various strain rates was shown to exhibit the same sigmoidal shaped curve seen for K_lc data in typical alloy steels.     

A THEORETICAL AND EXPERIMENTAL STUDY OF ENVIRONMENTAL HYDROGEN-ASSISTED SHORT FATIGUE CRACK GROWTH IN AN Al-Li ALLOY

Abstract— The initiation and propagation of fatigue cracks in an Al-Li 8090 alloy in a vapour environment of 0.6 M NaCl solution was investigated. A severe degradation of the resistance to short crack growth was exhibited. Preliminary work carried out to establish the susceptibility of the material to hydrogen embrittlement demonstrated a close correlation between the deformation mode of this alloy and hydrogen absorption. The combination of highly localized slip and highly localized hydrogen fugacity creates a high susceptibility to hydrogen-assisted crack growth.
On the basis of current micro-mechanical models, it is suggested that hydrogen trapping induces a reduction of the friction stress acting in the crack tip plastic zone. Consequently, enhanced plasticity at the crack tip due to the decrease in friction stress leads to an increase in crack growth rate.
An exact solution for a surface crack in a semi-infinite plane is obtained based on a dislocation crack model. Using this solution a computer method is developed to calculate the time-dependent short crack growth rate and fatigue lifetime. Both solutions show good correspondence with the experimental results.     

Orientation dependence of fracture in copper bicrystals with symmetric tilt boundaries

Experimental results (Wang and Anderson (1991), Acta Metall. 39, 779–792) show that the fracture behavior of Σ9 copper bicrystals depends on the cracking direction. Near-interface transgranular fracture surfaces were observed in the case of the crack growing in the [ 14] direction, with an essentially ductile failure mode, while the case of the crack growing in the [1 ] direction showed far less toughness and had an intergranular fracture surface with cleavage tongues. Asymptotic and finite element models for stationary cracks in ideally plastic and strain hardening materials have been used to examine this cracking direction dependency from a small strain continuum mechanics point of view. The tensile stress ahead of the crack tip was found to be essentially identical for the two growth directions, with the brittle orientation resulting in only slightly higher stress values at small distances from the crack tip. However, the strain field was found to be different for the two orientations, with the overall plastic zone size being much larger in the ductile case. Also, the orientations of the zones of concentrated shearing ahead of the crack, observed in the ideally plastic model, suggest two different dislocation shearing mechanisms. In the ductile case, this zone is parallel to the slip plane, resulting in a regular shearing mechanism in which dislocations can be nucleated at the crack tip and glide on the (111) slip plane. In contrast, this zone is perpendicular to the (111) slip plane in the brittle case, resulting in a kinking shear mode in which dislocations from other external sources expand in a dipole mode to produce macroscopically concentrated shearing. Thus, apart from the dislocation nucleation considerations, continuum mechanics does not seem to be able to fully explain this difference in directional dependency of fracture in the Σ9 copper bicrystals.     

The role of twinning–detwinning on fatigue fracture morphology of Mg–3%Al–1%Zn alloy

Typical fracture morphology of Mg–3%Al–1%Zn (AZ31) alloy after low cycle fatigue was investigated using SEM and optical microscope. It is shown that prolific lamellar structure in the crack initiation and crack stable propagation zone mainly results from twinning, while dimple structure formed in the unstable crack propagation and final rupture zone is mainly due to slip. The formation mechanisms of corresponding morphologies are proposed based on twinning and detwinning processes during compressive and tensile loading half cycles, respectively, for this alloy.     

Near-threshold fatigue crack growth at room temperature and an elevated temperature in Al---Li alloy 8090

The effects of slip distribution and crack tip shielding mechanisms on the near-threshold fatigue crack growth of the Al---Li alloy 8090 have been studied at both room temperature and an elevated temperature. The slip distribution has been varied by changing the distribution of the S phase, through prior stretching or by means of a duplex heat treatment. Fatigue crack growth (FCG) tests were conducted at a high stress ratio to reduce possible effects due to crack closure.

At room temperature the changes in FCG rates are interpreted as arising from the changes in the degree of planarity of slip in the materials.

At 150°C, the microstructural changes due to the long exposure to elevated temperature appear to dominate the effects observed. At lower ΔK, where the time at temperature is greatest, lower ΔK thresholds than those found at room temperature are obtained. These have been attributed to increased slip homogenization due to the increased precipitation and coarsening of the incoherent S phase together with loss of toughness due to the growth of coarse grain boundary phases and the formation of the associated δ′ precipitate free zone.

At higher ΔK, where the time at temperature is low and microstructural changes are minimal, slower FCG rates than those found at room temperature are obtaine. These are explained in terms of increased crack tip shielding which arises because of the increase in tortuosity of the crack path, the increased slip homogenization and the climb and cross-slip within the crack tip plastic zone.     

Investigation of process zone structure in Fe–3Si alloy

Abstract

An in situ fracture experiment was carried out in a scanning electron microscope to investigate plastic deformation and strain distribution in the process zone (PZ) located in the immediate vicinity of the crack tip in an Fe–3Si alloy (wt-%) under mixed mode loading conditions. It was observed that plastic deformation occurred by successive activation of a number of slip systems. The strain distribution and shape of the PZ were strongly dependent on the crystallographic orientation of the grain containing the crack tip. The distribution differed from that predicted using near tip blunting calculations and was best expressed by an exponential equation. Additional strain concentrations created by surface defects caused slight perturbations in the overall distribution. Crack propagation started along a coarse slip band which possessed the highest strain. It was found that the maximum strains in the PZ exceeded the uniaxial tensile fracture strain.

MST/1404     

Microstructurally-dependent model for predicting the kinetics of physically small and long fatigue crack growth

Based on the proposed concept of the fatigue threshold stress intensity factor ranges, a model has been developed that describes the kinetics of physically small fatigue crack and long fatigue crack growth. The model allows the calculation of the crack growth rate under the regular fully-reversed uniaxial loading from the data on the static characteristics of mechanical properties and the microstructure of the initial material. The crack depth at which the cyclic plastic zone size ahead of the crack tip will exceed the grain size should be considered as a criterion of the small-to-long crack transition. Under high-cycle fatigue conditions physically small fatigue crack growth will be divided into two phases of growth: the first phase is when the crack propagates along the slip planes of individual grains, and the second one is when the crack changes the mechanism of growth and propagates in the plane perpendicular to the loading direction. The model validity has been tested using the experimental data on the growth of the long cracks in specimens of titanium alloy VT3-1 in seven microstructural states and the small cracks in specimens of titanium alloy Ti–6Al–4V and aluminum alloy 2024-T3. Good agreement between the calculated and experimental results is obtained.     

Analysis of the Elastoplastic Deformation of the Material in the Process Zone

By the method of digital correlation of speckle images, we record the displacements in the vicinity of the crack tip in plane specimens of D16AT alloy. The field of elastoplastic displacements is determined in the vicinity of the crack tip under static loading. By using the distribution of displacements, we compute the levels of strains ε _y on the continuation of the crack. The theoretical results are in good agreement with the experimental data in estimating the length of the plastic zone for the limiting equilibrium state.__________Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 40, No. 5, pp. 67–72, September–October, 2004.     

外应力场下NiAl合金微裂纹动态扩展的分子动力学模拟

目的 对NiAl合金中不同晶体取向的裂纹扩展动力学行为进行原子尺度研究,明晰在塑性变形过程     

On the Cohesive Zone Model for a Finite Crack

The paper concentrates on the development of the crack tip model with the cohesive zone in an infinite plate with a finite crack of mode I. The estimation of the length of the cohesive zone and the crack tip opening displacement is based on the comparison of the local stress concentration according to Westergaard's theory with the cohesive stress. To calculate the cohesive stress, von Mises yield condition at the boundary of the cohesive zone is employed for plane strain and plane stress. The model of the stress distribution with the maximum stress within the cohesive zone is discussed. The calculation results of the crack tip opening displacement are compared with the Dugdale solution for the plane stress. This revised version was published online in July 2006 with corrections to the Cover Date.     

Experimentelle Charakterisierung und zweidimensionale Simulation der mikrostrukturbestimmten Ermüdungsrissausbreitung in einer β‐Titanlegierung

In this project the initiation and propagation of short fatigue cracks in the metastable β‐titanium alloy TIMETAL®LCB is investigated. By means of an interferometric strain/displacement gauge system (ISDG) to measure the crack opening displacement (COD) and the electron back scattered diffraction technique (EBSD) to determine the orientation of individual grains the microstructural influence on short crack initiation and growth can be characterized. Finite element calculations show a high influence of the elastic anisotropy on the initiation sites of cracks. Crack propagation takes place transgranulary along slip planes as well as intergranulary along grain boundaries. The crack growth rate depends strongly on the active mechanism at the crack tip which in turn is influenced by crack length, the applied stress and the orientation of the grains involved. The value of the steady state crack closure stress changes from a positive value at low applied stresses (roughness induced) to a negative one at higher applied stresses (due to plastic deformations at the crack tip). The crack growth simulation is realised by a two‐dimensional boundary element technique, which contains the ideas of Navarro und de los Rios. The model includes the sequence of the applied stress amplitude as well as the experimental measured roughness induced crack closure.     

The range of applicability of the small-scale yielding approach in theoretical investigations of yield and fracture at a crack tip

Theoretical analysis of the processes of plastic deformation and fracture in the vicinity of a sharp crack tip becomes easier if plasticity is confined to the immediate vicinity of the crack tip, for linear elastic stress intensity factors can be used to give the surrounding elastic field, and it is possible to employ a boundary layer formulation to determine the elastic-plastic field in the immediate vicinity of the crack tip. Consideration is given to the range of applicability of the small-scale yielding approach using a simple model in which slip is confined to the crack plane. A range of stress-displacement laws is considered, the object being to assess the effect of a material's flow characteristics on the range of applicability. The conclusions are discussed with respect to plane strain crack propagation in mild steel.     

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.     

A theoretical model for roughness induced crack closure

A theoretical model for the effects of grain size on the magnitude of roughness induced crack closure (RICC) at fatigue crack growth threshold has been proposed. With the basic configuration of a crack propagating incrementally along planar slip bands and deflecting at grain boundaries, an idealized zig-zag crack path is considered. The effective slip band length is considered to be equal to grain size. It is assumed that the dislocations emitted from the crack tip upon loading to form the pile-up are completely irreversible to produce a comnined mode I and mode II displacement at the crack tip. The assumption of continuously distributed dislocations in the pile-up facilitated the calculation of crack tip sliding displacement (CTSD) along the slip plane from which the mode I closure disregistry just behind the crack tip can be calculated. The closure stress intensity factor at threshold, K _el,th could then be expressed as a function of critical resolved shear stress, average macroscopic yield stress, angle subtended by the slip plane with the crack plane and the length of the slip band. Comparisons of the predicted trends with experimental data from various alloy systems indicate good agreement.

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Résumé On propose un modèle théorique pour décrire les effets de la taille du grain sur l'importance de la rugosité associée à la fermeture d'une fissure lors du franchissement du seuil de propagation en fatigue. On considère un chemin de fissuration en zig-zag idéalisé, avec une configuration de base d'une fissure qui se propage par incréments le long des bandes de glissements et par déviations aux frontières des grains. La longueur effective d'une bande de glissement est prise comme égale à la taille du grain. On suppose que les dislocations émises de l'extrémité de la fissure sous charge et qui forment l'empilement, sont totalement irréversibles au point de produire un déplacement combiné de mode-I et de mode-II à cette même extrémité. L'hypothèse de dislocations continûment distribuées dans l'empilement facilite le calcul du dèplacement par glissement de l'extrémité de la fissure le long du plan de glissement, à partir duquel on peut établir les conditions de fermeture en mode-I juste derrière l'extrémité de la fissure. Le facteur d'intensité de contraites de seuil peut dès lors être exprimé en fonction de la contrainte critique de cisaillement, de la limite élastique macroscopique moyenne, de l'angle entre le plan de glissement et le plan de la fissure, et de la longueur de la bande de glissement. Un bon accord est trouvé entre les tendances prévues et les données expérimentales, dans le cas de divers alliages.

     

Fatigue crack growth retardation under constant amplitude and variable mean stress

Fatigue crack growth retardation under stress spectra with constant amplitude and variable mean stress, respectively, was studied. Flat specimens with a central through crack were tested under tension-tension load. The specimens were made with low alloy steel 4 mm thick, with yield strength of 625 Mpa and ultimate tensile strength of 784 MPa. Overload affected crack length increments Δa¹ were studied. The best correlation was obtained between monotonic plane stress plastic zone size 2r_y and Δa¹. The cyclic plastic zone size 2r_pc correlated with crack length increment of minimum crack growth rate after overload. Forman's equation and Willenborg's model of fatigue crack growth retardation were used for theoretical prediction of fatigue crack propagation life. The best agreement between theoretical and experimental results was also obtained using monotonic plastic zone size instead of monotonic plastic zone radius or cyclic plastic zone size. The agreement is reasonably good, even though in the case of one spectrum, cracks were arrested for several thousand cycles.     

高周疲劳载荷下6061-T6铝合金的温度演化

为了研究金属材料在疲劳载荷下的温度变化,采用红外热像系统对高周疲劳载荷下6061-T6铝合金的温度演化进行分析,用热像图对疲劳裂纹尖端的塑性区进行测量.结果显示,疲劳加载作用下,循环次数达到107次时6061-T6铝合金试样表面温度的变化分为四个阶段:初始温升阶段、温度缓降阶段、温度二次缓慢上升阶段和温度快速上升阶段.结合热弹性理论、铝合金塑性变形的微观机制分析并预测疲劳载荷下温度的演化和宏观裂纹扩展时裂纹尖端塑性区域大小.宏观裂纹开始扩展时,裂纹尖端的塑性区域可达3.6 mm2,红外热像仪测得结果为3.46 mm2,测试结果与理论结果吻合.     

Steady-state crack growth and fracture work based on the theory of mechanism-based strain gradient plasticity

Mode I steady-state crack growth is analyzed under plane strain conditions in small scale yielding. The elastic-plastic solid is characterized by the mechanism-based strain gradient (MSG) plasticity theory [J. Mech. Phys. Solids 47 (1999) 1239, J. Mech. Phys. Solids 48 (2000) 99]. The distributions of the normal separation stress and the effective stress along the plane ahead of the crack tip are computed using a special finite element method based on the steady-state fundamental relations and the MSG flow theory. The results show that during the steady-state crack growth, the normal separation stress on the plane ahead of the crack tip can achieve considerably high value within the MSG strain gradient sensitive zone. The results also show that the crack tip fields are insensitive to the cell size parameter in the MSG theory. Moreover, in the present research, the steady-state fracture toughness is computed by adopting the embedded process zone (EPZ) model. The results display that the steady-state fracture toughness strongly depends on the separation strength parameter of the EPZ model and the length scale parameter in the MSG theory. Furthermore, in order for the results of steady crack growth to be comparable, an approximate relation between the length scale parameters in the MSG theory and in the Fleck-Hutchinson strain gradient plasticity theory is obtained.