Maximum Plastic Zone Size Research Articles

Numerical simulations of mixed-mode (I and II) notch tip fields in basal-textured magnesium alloys

Crystal plasticity based finite element (CPFE) simulations employing Taylor homogenization for a basal-textured Mg alloy are performed under plane strain, small scale yielding (SSY) conditions to study mixed-mode (I and II) notch tip fields. Two notch orientations are considered. In one case, the notch line and normal to the flat surfaces of the notch are taken parallel to the transverse direction (TD) and rolling direction (RD), whereas in the other, they are aligned with normal direction (ND) and TD. The results are compared against those obtained from an isotropic (von Mises) plasticity model with identical stress–strain behavior under RD tension. The maximum plastic zone size at a given level of effective stress intensity factor |K|, enhances with mode II component (i.e., with decrease in mode mixity parameter Me), and is larger for ND–TD orientation. Further, {101̄2} or tensile twinning (TT) occurs near the stretched part of the notch surface, and is more profuse as Me reduces especially for the ND–TD case. It is found that for a given Me, the notch orientation can profoundly affect the distribution of equivalent plastic strain and hydrostatic stress around the notch tip, which underscores the importance of plastic anisotropy of Mg alloys. Finally, by employing appropriate fracture criteria and the computed near-tip fields, the variations of fracture toughness and operative fracture mechanism with Me are predicted for the TD–RD case, which corroborate well with a recent experimental study.

Mixed-mode (I/II) crack initiation direction for elastic-plastic materials based on crack-tip plastic zone

In this paper, crack-initiation direction for an elastic-plastic material (interstitial free steel) under mixed-mode (I/II) load is studied based on crack-tip plastic zone under monotonic load. The feasibility of using the minimum plastic zone radius (MPZR) criterion for elastic-plastic materials is also examined. The shape and size of crack-tip plastic zones have been estimated by elastic-plastic finite element analysis in a plane stress single edge notch tensile (SENT) specimen under mixed-mode (I/II) loading according to von Mises yield criteria. The results show that the minimum plastic zone sizes were not clearly identified; indicating MPZR criterion is not suitable for the analysis of elastic-plastic materials. It is shown that the crack initiation direction for elastic-plastic materials depends on the path of the maximum plastic zone size. The variation of crack initiation angle is also studied with respect to mode mixity factor and the results are found to be in good agreement with the experimental results available in the literature.

3D finite element analysis on crack-tip plastic zone

This paper presents an effect of specimen thickness on crack-tip plastic zone shape and size. The shape of the plastic zone is estimated in 3D with the help of elastic and elastic-plastic finite element analyses. The results indicate that the shape of plastic zone does not correspond to classical “dog-bone shape” and the maximum plastic zone size occurs beneath the free surface, contrary to conventional shape. It is observed that for specimens with B/W=0.5, the ASTM requirement of specimen thickness to estimate KIC, the plastic zone shape and size is much larger than the one obtained in 2D plane strain analysis. The results also show a significant change in the shape and size of plastic zone in elastic and elastic plastic conditions. International Journal of Engineering, Science and Technology, Vol. 2, No. 6, 2010, pp. 47-58

The influence of modified intermetallics and Si particles on fatigue crack paths in a cast A356 Al alloy

Mechanical fatigue tests were conducted on uniaxial specimens machined from a cast A356‐T6 aluminium alloy plate at total strain amplitudes ranging from 0.1 to 0.8% (R = − 1). The cast alloy contains strontium‐modified silicon particles (vol. fract. ~6%) within an Al–Si eutectic, dispersed α intermetallic particles, Al15 (Fe,Mn)3 Si2 (vol. fract. ~1%), and an extremely low overall volume fraction of porosity (0.01%). During the initial stages of the fatigue process, we observed that a small semicircular fatigue crack propagated almost exclusively through the Al–1% Si dendrite cells. The small crack avoided the modified silicon particles in the Al–Si eutectic and only propagated along the α intermetallics if they were directly in line with the crack plane. These growth characteristics were observed up to a maximum stress intensity factor of ~K trmax = 7.0 MPa m1/2 (maximum plastic zone size of 96 μm). When the fatigue crack propagated with a maximum crack tip driving force above 7.0 MPa m1/2 the larger fatigue crack tip process zone fractured an increased number of silicon particles and α intermetallics ahead of the crack tip, and the crack subsequently propagated preferentially through the damaged regions. As the crack tip driving force further increased, the area fraction of damaged α intermetallics and silicon particles on the fatigue fracture surfaces also increased. The final stage of failure (fast fracture) was observed to occur almost exclusively through the Al–Si eutectic regions and the α intermetallics.

Effect of Stress Ratio on Short Fatigue Crack Growth

A model of short fatigue crack growth is proposed, which is based on the blocked slip concept and the shear decohesion mechanism. The analysis is extended to the case of mean stress loading. A theoretical proof is presented for the transfer of slip bands across grain boundaries. The rate of growth is proportional to the shear strain range and the maximum plastic zone size. There are no adjustable parameters in the theory for the case of high strain level, when the plastic strain dominates the decohesion process. Otherwise only one constant is needed, which may be derived from long crack growth data. The model is shown to provide satisfactory predictions of experimental results under uniaxial loading with various stress amplitudes and mean stresses.

On the particle-size dependence of fatigue-crack propagation thresholds in SiC-particulate-reinforced aluminum-alloy composites: Role of crack closure and crack trapping

A study has been made of ambient-temperature fatigue-crack propagation behavior in P/M Al-Zn-Mg-Cu metal-matrix composites reinforced with either 15 or 20 vol.% silicon-carbide particulate, with specific emphasis on the role of SiC-particle size on the fatigue-crack growth threshold condition. It is found that measured threshold stress-intensity levels ΔK TH , are a function of both SiC-particle size and volume fraction; however, whereas coarse-particle distribution results in higher ΔK TH values at low load ratios, fine particles give higher threshold at high load ratios. Such behavior is analyzed in terms of the interaction of SiC particles with the crack path, both in terms of the promotion of (roughness-induced) crack closure at low load ratios and by crack trapping by particles. Consideration of the latter mechanism yields a limiting requirement for the intrinsic threshold condition in these materials that the maximum plastic-zone size must exceed the effective mean particle size; this implies that for near-threshold crack advance, the tensile stress in the matrix must exceed the yield strength of the material beyond the particle.

Effect of grain size on the near threshold fatigue crack propagation of a nickel base precipitation hardened superalloy

1. 1. By coarsening the grain size from 22 to 91 μm in Alloy 718, it was found that: i. near threshold crack growth rates were reduced and ii. ΔK th values increased. 2. 2. Roughness-induced crack closure may be used to explain the influence of grain size. The coarse grained material resulted in much rougher fracture surfaces at near threshold growth rates. 3. 3. At room temperature, a fracture morphology transition occurred which coincided with the concave upward ergion in the crack growth curves above ΔK th. Below the transition, the maximum plastic zone size was less than the grain diameter and the crack propagated by crystallographic cracking. Above the transition in which the maximum plastic zone size was greater than the grain diameter, crack extension occurred through the formation the formation of fatigue striations. This transition was shifted to higher ΔK values by coarsening the grain size.

Plastic deformation around a fatigue crack near threshold in 3%SiFe

Fatigue crack propagation tests were conducted on 3%SiFe polycrystals at different stress ratios, and the plastic deformation around fatigue cracks revealed by the etch pit technique is discussed quantitatively in combination with the measurement of crack closure. In the high rate region, region B, the maximum plastic zone size was predictable from the fracture mechanics equation where the friction stress was substituted for the monotonic yield stress. Near the threshold, in region A, it tended to be smaller than that given by the equation established in region B. The increase in the crack closure was remarkable in region A. The size of the highly strained region correlated better with the effective stress intensity range than with the total stress intensity range in both regions A and B. The crack propagation rate was expressed as a power function of the highly strained zone size, and the threshold condition corresponded to the constant size of the highly strained region.

The effect of load ratio on the threshold stresses for fatigue crack growth in medium carbon steels

A study of the effect of load ratio, R, on the low crack growth rates and the threshold stress conditions exhibited by five medium carbon steels has been conducted. It was found that decreased values of R retarded crack growth to an increasing degree as a defined threshold for crack growth was approached, such that this threshold showed a marked dependence on K max rather than ΔK. Comparisons of the five materials showed that the threshold increased as yield strength increased for a given R, but this effect could be normalised in terms of a constant value of the maximum plastic zone size at the crack tip.