Effect of defect orientation on metal fracture-statistical prognosis

Aluminium specimens of pre-caused defects are tensile tested at different temperatures. The defects are differently oriented to the tensile axis. The results have undergone statistical processing integrated with fundamental fracture approach. Analytical model to prognosticate the metal reliability in the range of applied tensile stresses is found. A method for evaluation of the defects orientation effect on fracture is suggested. The introduced strength spaces present a principal strength history of loaded defect metal.     

Effect of lattice orientation on crack tip constraint in ductile single crystals

In this work, the effect of lattice orientation on the fields prevailing near a notch tip is investigated pertaining to various constraint levels in FCC single crystals. A modified boundary layer formulation is employed and numerical solutions under mode I, plane strain conditions are generated by assuming an elastic–perfectly plastic FCC single crystal. The analysis is carried out corresponding to different lattice orientations with respect to the notch line. It is found that the near‐tip deformation field, especially the development of kink or slip shear bands is sensitive to the constraint level. The stress distribution and the size and shape of the plastic zone near the notch tip are also strongly influenced by the level of T ‐stress. The present results clearly establish that ductile single crystal fracture geometries would progressively lose crack tip constraint as the T ‐stress becomes more negative irrespective of lattice orientation. Also, the near‐tip field for a range of constraint levels can be characterized by two‐parameters such as K–T or J–Q as in isotropic plastic solids.     

Significance of limiting (equivalent) tip radius and crack tip deformation for cleavage induced fracture in structural steels

In two structural steels, the limiting crack tip radius (LTR) and the crack tip blunting radius have been evaluated at the instant of fracture initiation by cleavage. The effect of yield strength on LTR and the blunting radius has been investigated. The relationship between the limiting and the blunting tip radius has been studied. The limiting tip radius has been found to be of the order of the plastic zone radius in the structural steels investigated     

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.     

Thickness effect on crack tip deformation at fracture

The crack tip deformation at the onset of surface crack growth for four single edge cracked specimens having four different thicknesses were studied. The specimens were made of the ductile and tough HY-80 steel. The thickness contraction in the crack tip region and the tensile strain in the direction of load were measured. The crack tip necking-in acts like a notch. The depths, the root radii, and the angle changes of the necking-in notches were measured. The results indicated that the near tip strain can be used as a fracture criterion of ductile and tough materials. It was also found that the fracture strengths of the cracked specimens can be correlated with the tensile ductilities measured with Clausing specimens.     

Effect of crack closure on non-linear crack tip parameters

Crack closure concept has been widely used to explain different issues of fatigue crack propagation. However, some authors have questioned the relevance of crack closure and have proposed alternative concepts. The main objective here is to check the effectiveness of crack closure concept by linking the contact of crack flanks with non-linear crack tip parameters. Accordingly, 3D-FE numerical models with and without contact were developed for a wide range of loading scenarios and the crack tip parameters usually linked to fatigue crack growth, namely range of cyclic plastic strain, crack tip opening displacement, size of reversed plastic zone and total plastic dissipation per cycle were investigated. It was demonstrated that: (i) LEFM concepts are applicable to the problem under study; (ii) the crack closure phenomenon has a great influence on crack tip parameters decreasing their values; (iii) the ΔK_eff concept is able to explain the variations of crack tip parameters produced by the contact of crack flanks; and (iv) the analysis of remote compliance is the best numerical parameter to quantify the crack opening level. Therefore the crack closure concept seems to be valid. Additionally, the curves of crack tip parameters against stress intensity factor range obtained without contact may be seen as master curves.     

The DFZ model of fracture at crack tip and crack initiation criterion

Direct observation by transmission electron microscopy (TEM) has been made on the distribution of dislocations in front of the crack tip during tensile deformation of aluminum. A microfracture model has been established to describe the equilibrium configuration of the dislocations in the presence of a dislocation-free zone (DFZ). The site of void nucleation observed from TEM experiments was found to be at about the place of maximum dislocation density predicted from the model. The relationship between the size of crack, DFZ and crack opening displacement (COD) was obtained as a function for a crack initiation criterion.     

The effects of constraint on crack tip fields and fracture toughness

The detailed stresses, deformations and porosities in the vicinity of a blunting crack in different fracture specimens, Single Edge Notch (SEN), Three Point Bending (TPB) specimens, and Small Scale Yielding (SSY) model were studied by the larger deformation finite element method. The presence and subsequent growth of smaller scale voids were taken into account by using a modified Gurson's model to describe the constitutive behavior of the material. The dependences of the stresses, deformations and porosities on specimen configurations were associated with the crack tip constraint. The porosity in the tip region, along with the void coalescence criterion, were used to predict the macroscopic fracture toughness as a function of the constraint, and a comparison with experimental data was performed in this paper.     

An FEM study on crack tip blunting in ductile fracture initiation

Ductile fracture is initiated by void nucleation at a characteristic distance (I_c) from the crack tip and propagated by void growth followed by coalescence with the tip. The earlier concepts expressed I_c in terms of grain size or inter-particle distance because grain and particle boundaries form potential sites for void nucleation. However, Srinivas et al. (1994) observed nucleation of such voids even inside the crack tip grains in a nominally particle free Armco iron. In an attempt to achieve a unified understanding of these observations, typical crack-tip blunting prior to ductile fracture in a standard C(T) specimen (Mode I) was studied using a finite element method (FEM) supporting large elasto-plastic deformation and material rotation. Using a set of experimental data on Armco iron specimens of different grain sizes, it is shown that none of the locations of the maxima of the parameters stress, strain and strain energy density correspond to I_c. Nevertheless, the size of the zone of intense plastic deformation, as calculated from the strain energy density distribution ahead of the crack tip in the crack plane, compares well with the experimentally measured I_c. The integral of the strain energy density variation from the crack tip to the location of void nucleation is found to be linearly proportional to J_IC. Using this result, an expression is arrived at relating I_c to J_IC and further extended to CTOD_c.     

Relationship between fracture toughness and deformation ahead of the crack tip

An analytical relationship for the calculation of the intensity of elastoplastic strains at the front of a mode I crack is obtained on the basis of the suggested model. A strain criterion of fracture toughness has been developed which relates the stress intensity factor to the width of the stretch zone, the mechanical properties of the material, and its elastic constants. A comparison of experimental and numerical (obtained by using the proposed equations) data of the stretch zone width for 15Kh2NMFA steel in a wide temperature range demonstrates good agreement between the theory and the experiment. This proves the possibility of calculating fracture toughness via the stretch zone width and mechanical properties of the material. Translated from Problemy Prochnosti, No. 2, pp. 33–40, March–April, 1997.     

Effect of stress triaxiality levels in crack tip regions on the characteristics of void growth and fracture criteria

The behaviour of void growth in the crack tip regions of four specimen geometries with different stress triaxiality levels have been investigated by the FEM method and experimental observations in plane strain and plane stress cases respectively. It was found that the shape change of growing voids, the configurations of a blunting crack tip and the sizes of decreasing ligament between the void and the crack tip are strongly dependent upon the stress triaxiality levels. Under the condition of plane stress, the stress triaxiality on the ligaments of cracks are nearly the same for different specimen geometries, also the void growth, crack tip blunting asnd decreasing of ligament size are identical for various specimens with increasing load levels, which lead to the conclusion that the J_i-value is independent of specimen geometries. However, in the plain strain case, different void growth, crack tip blunting and decreasing in ligament size for various stress triaxiality levels directly caused the J_i-value to be dependent on the specimen geometries. It was found that when the void is linked to the blunting crack tip by the extrapolation to the zero ligament from FEM calculations, the J_i values, measured experimentally, are underestimated slightly.     

Modeling of crack tip high inertia zone in dynamic brittle fracture

A phenomenological modification is proposed to the existing cohesive constitutive law of Roy and Dodds to model the crack tip high inertia region proposed by Gao. The modification involves addition of a term which is attributed to fracture mechanisms that result in high energy dissipation around the crack tip. This term is assumed to be a function of external energy per unit volume input into the system. Finite element analysis is performed on PMMA with constant velocity boundary conditions and mesh discretizations based on the work of Xu and Needleman. The cohesive model with the proposed dissipative term is only applied in the high inertia zone and the traditional Roy and Dodds model is applied on cohesive elements in the rest of the domain. The results show that crack propagates in three phases with a speed of 0.35c_R before branching, confirming experimental observations. The modeling of high inertia zone is one of the key aspects to understanding brittle fracture.     

The influence of crystallographic orientation on crack tip displacements of microstructurally small, kinked crack crossing the grain boundary

The paper presents an analysis of the effects of grain orientations on a short, kinked surface crack in a 316L stainless steel. The kinking of the crack is assumed to take place at the boundary between two neighbouring grains. The analysis is based on a plane-strain finite element crystal plasticity model. The model consists of 212 randomly shaped, sized and oriented grains, loaded monotonically in uniaxial tension to a maximum load of 0.96R_p0.2 (240 MPa). The influence that a random grain structure imposes on a Stage I crack is assessed by calculating the crack tip opening (CTOD) displacements for bicrystal as well as for polycrystal models, considering different crystallographic orientations. Since a Stage I crack is assumed, the crack is always placed in a slip plane. Results from a bicrystal case show that the maximal CTODs are directly related to the stiffness of the grain containing the crack extension. Anisotropic elasticity and crystal plasticity both contribute to this grain stiffness, resulting in maximal CTOD when Schmid factors are the highest on two slip planes. Such crystallographic orientation results in a soft elasto-plastic response. Anisotropic elasticity can additionally increase the softness of a grain at certain crystallographic orientations. Minimal anisotropic elasticity at the crystallographic orientations with the highest Schmid factors causes the CTOD to be maximized. Presuming that the crack will preferably follow the slip plane where the crack tip opening displacement is highest, we show that the crystallographic orientation can affect the CTOD values by a factor of up to 7.7. For a given grain orientation the maximum CTOD is attained when the crack extension deflection into a second grain is between −75.141° and 34°. For the polycrystal case we show that grains beyond the first two crack-containing grains change the CTOD by a factor of up to 3.3 and that the largest CTODs are obtained when placing the crack into a slip plane with crack extension that results in a crack extension being more perpendicular to the external load.     

The stress field near the blunt crack tip and the fracture criterion

The asymptotic expansion solution containing two terms for the stress field near the blunt crack tip is obtained. It is proposed that the slit be divided into the ideal crack, blunt crack I, blunt crack II and the notch in accordance with the geometrical structure of the slit tip. Whether the blunt crack can be considered as the ideal crack will depend mainly on the following three factors: $\text{√}\text{2R}{}_0\text{C}$, $\text{√}\text{R}{}_0\text{r}{}_{\mathrm{c}}$ and the profile of the crack. In this paper, the influence of the crack tip radius on the fracture criterion is studied and it is shown that the classical strength theories belong to the unconditional extremum criteria while the S criterion, etc. in fracture mechanics belong to the conditional extremum criteria. A modified maximum tension stress theory is developed, in which the fracture theories of the crack and the notch can be roughly unified.     

导电薄板内裂纹尖端区域的电磁应力

为了研究电磁应力对导电薄板内裂纹尖端的作用,从基本电磁理论出发,通过对导体表面所受电场力的分析,推得了导电薄板内裂纹边缘处电场力的表达式.在此基础上,通过导电薄板内裂纹尖端区域磁场的确定,得到裂纹尖端区域的电磁应力表达式.裂纹尖端电磁应力的计算表明,金属薄板中裂纹尖端的电磁应力是由裂纹尖端指向金属内部的压应力,并且当电流密度为103～104A/mm2的数量级时,裂纹尖端的压应力数值可达数兆帕到数百兆帕.因此,在研究裂纹止裂问题上,其影响不容忽视.     

XFEM fracture analysis of shells: The effect of crack tip enrichments

In this study the effect of crack tip enrichment functions in the extended finite element analysis of shells is investigated. Utilization of crack tip enrichments leads to reduction of the required number of elements, mesh independency and increased accuracy in computation of fracture mechanics parameters such as the stress intensity factor, the crack tip opening displacement and the crack tip opening angle. The procedure is verified by modeling various shell and plate problems and available benchmark tests. Also, effects of enrichments of in-plane, out-of-plane and rotational degrees of freedom and high order out-of-plane enrichments on different fracture modes are studied. Moreover, reduction of the dependency of crack tip opening angle on the element size in crack propagation problems is discussed.