Crack Tip Plastic Blunting Research Articles

Mechanistic model for hydrogen accelerated fatigue crack growth in a low carbon steel

Fracture by hydrogen accelerated fatigue crack growth is a severe type of environmental failure. Although fatigue crack growth has been the subject of intense investigation over several decades, a complete mechanistic and predictive model is still lacking. Such a crack growth model is even more rare in the case of hydrogen in view of the lack also of constitutive models for material deformation under cycling loading that account for the hydrogen effect. In this study, we present a model for fatigue crack propagation induced by alternating crack tip plastic blunting and re-sharpening, which in the presence of hydrogen can be accelerated by hydrogen enhanced dislocation motion and generation. The Chaboche constitutive model, which is a nonlinear kinematic hardening model capable of capturing many features of material behavior under cyclic loading, is used for the calculation of the stress and strain fields at the propagating crack tip. The Chaboche model is calibrated using a sequence of experimental data from uniaxial strain-controlled cyclic loading tests and uniaxial stress-controlled ratcheting tests with a low carbon steel, JIS SM490YB, in the absence and presence of hydrogen. The numerical simulation results indicate that the proposed crack propagation model can predict Paris law behavior and can successfully demonstrate acceleration of fatigue crack growth in the presence of hydrogen. Significantly, the profiles of the steady-state opening stress and strain ahead of the fatigue crack tip in a compact tension (C(T)) specimen were found to have sections over which they vary as ln(1/r) with distance r from the crack tip, consistent with the crack-tip strain field for a non-stationary crack.

On the theoretical modeling of fatigue crack growth

Although fatigue is by far the most common mode of failure of structural materials, mechanistic understanding is still lacking. For example, the fundamental Paris law which relates the crack growth rate to stress-intensity factor range is still phenomenological and no reliable mechanistic model has been established for a given material or class of materials despite numerous investigations over a half a century. This work is an attempt to theoretically model fatigue crack propagation induced by alternating crack-tip plastic blunting and re-sharpening in the mid-range of growth rates on the basis of inputs from experiments that measure macroscopic material behavior, e.g., response to uniaxial cycling loading. In particular, we attempt to predict Paris law behavior by accounting for the material constitutive behavior in response to cyclic loading by modeling crack advance solely in terms of the underlying plastic dissipation. We obtain the steady-state condition for crack growth based on plastic dissipation, numerically using finite element analysis, which involves a methodology to address plastic closure upon unloading. For a given stress-intensity range, we calculate the crack propagation rate from the steady-state condition through each cycle of loading and unloading of a cracked compact-tension specimen, without resorting to any specific criterion for crack advance.

Simulation of fatigue crack growth by crack tip plastic blunting using cohesive zone elements

The propagation of a fatigue crack in 2D specimens by crack tip plastic blunting is simulated by using a Finite Element implementation of the strip-yield model. At each cycle, the crack growth is assumed to result from the variation of the Crack Tip Opening Displacement (ΔCTOD). The implementation is based on cohesive elements with an elastic perfectly plastic behavior, which allows to simulate, the crack closure phenomena due to the plastic wake behind the crack tip. A mesh sensitivity analysis provides the minimum number of elements requested in the crack tip plastic zone for a given accuracy. Then, the advance scheme based on crack tip blunting is described. Finally, the variation of the opening load with respect to the load ratio R, and to the maximum load is investigated and compared with analytical results.

Effect of Copper Content on the Microstructures and Properties of TiB<sub>2</sub> Based Cermets by SHS

TiB2 based cermets with different copper content were produced from titanium powder, boron powder and copper powder by Self-propagating High-temperature Synthesis under conditions of Pseudo Hot Isostatic Pressing (SHS/PHIP). In order to obtain the optimal copper content, the effect of copper content on the microstructures and properties of TiB2 based cermets was investigated. The size of the TiB2 particles in the products decreased with increasing amounts of copper. The hardness (HRA) and bend strength increased firstly, then decreased with copper increasing. Their maximum values appeared at 20 wt.% and 40 wt.% copper, respectively. The porosity of TiB2 based cermets decreased with the copper content increasing due to good fluidity of copper. With the addition of copper, the fracture toughness of TiB2 based cermets increased gradually. Crack-tip plastic blunting by a ductile metallic phase and crack deflection are the principal mechanisms of toughness improvement of TiB2 based cermets. The range of optimal copper content in the TiB2 based cermets is between 40 wt.% and 50 wt.%.

Combustion synthesis and densification of titanium diboride–copper matrix composite

The quasi-static consolidation in uniaxial compression of combustion synthesized TiB 2–Cu composite with 40 wt.% Cu from Ti, B and Cu powders was investigated. Thermodynamics of the system was calculated theoretically. It was found that TiB 2 was a stable phase in the composite and TiCu interphase compound can convert into stable phase. The phases of the synthesized product were identified using X-ray diffraction and the results showed only TiB 2 and Cu phases, no other phases existed in the product. It is consistent with the calculated result of thermodynamics. The consolidated product was dense and no apparent pores existed in the microstructure. Fine TiB 2 reinforcement grows in near equivalent axis-like and block-like shapes. As a binder phase, copper metal was found between TiB 2 and TiB 2 particles. It is shown that copper improves the densification behavior during combustion synthesis, compared with synthesized pure TiB 2 ceramic. Due to the addition of copper, the relative density, bend strength and fracture toughness of TiB 2–Cu composite are much higher than those of TiB 2 ceramic. Crack-tip plastic blunting by a ductile metallic phase and crack deflection by the stress due to the difference of thermal expansion coefficient and elastic modulus between TiB 2 and Cu are the principal mechanisms of toughness improvement of TiB 2–Cu composite.

Plastic deformation at the tip of a tensile crack in a non-linear kinematic hardening material

The plastic deformation at the tip of a tensile crack in a non-linear kinematic hardening material under small-scale yielding conditions is investigated, with a view to quantifying the functional dependence of crack-tip plastic blunting size on material's strain hardening parameters. It is shown by dimensional analysis that, for materials being characterised by the Armstrong-Frederick non-linear kinematic hardening rule, the crack-tip blunting parameter depends parametrically on only two non-dimensional parameters; the functional dependence is determined using a parametric finite element analysis.

Crack-tip plastic blunting under gross section yielding and implications for modelling physically short cracks

The plastic blunting behaviour at the tip of a mode I crack embedded in a grossly plastic material is analysed, with a view to identifying a consistent scaling parameter for correlating the growth rates of short and long fatigue cracks. Numerical analysis is first carried out using a finite element method that accounts for the large deformation and non-proportional straining near the crack tip. It is found that the crack-tip plastic blunting is uniquely characterized by a single size scale, despite the fact that the J-dominance on the stress-strain field exists only at a distance greater than the crack-tip opening displacement. An improved formula is constructed based on the finite element results to relate this size scale to the remote loading and the materials' cyclic deformation properties. A solution has been derived to quantify the influence of cyclic plasticity on the closure of short cracks, which is shown to correlate well with experimental results. When plotted in terms of the present crack-tip blunting parameter, the growth rates of physically short cracks seem to fall within a band comparable to the scatter band of the experimental data.

Crack-tip plastic blunting under gross section yielding and implications for modelling physically short cracks

Crack-tip plastic blunting under gross section yielding and implications for modelling physically short cracks

The influence of cross‐sectional thickness on fatigue crack growth

For thin structures, fatigue crack growth rates may vary with the structure's thickness for a given stress intensity factor range. This effect is mainly due to the change in the nature of the plastic deformation when the plastic zone size becomes comparable with, or greater than, the cross‐sectional thickness. Variations in the constraint affect both the crack tip plastic blunting behaviour as well as the fatigue crack closure level. Approximate expressions are constructed for the constraint factor based on asymptotic values and numerical results, which are shown to correlate well with finite element results. It is demonstrated that the present results not only permit predictions of the specimen thickness effects on fatigue crack propagation under spectrum loading, but also eliminate the need to determine the constraint factor by curve‐fitting crack growth data.

HIGH TEMPERATURE FATIGUE IN SINGLE CRYSTAL SUPERALLOYS

Abstract— The growth rate of fatigue cracks in two single crystal nickel base superalloys, CMSX‐6 and SRR99, along the <001> planes are presented and rationalised in terms of two interacting crack propagation mechanisms: one attributed to crack tip plastic blunting and the other attributed to the brittle failure of the oxide scales. The role of the oxide scale is twofold as it also wedges the crack and modifies the blunting term through a crack closure effect. On the other hand, a positive effective stress intensity range is required to fracture the oxide scale. Fatigue tests were carried out at different temperatures (500 to 1050°C), frequencies (0.001 to 20 Hz), cycle waveforms and load ratios (0 to 0.9), with starter crack lengths of abut 100 μm. The model predictions match the crack growth rates obtained for both materials. Even though both materials are nickel base superalloys, they have very different oxidation behaviours. CMSX‐6 has an improved oxidation resistance over SRR99, however, because of the twofold nature of the oxidation process, which material provides the better life expectancy depends on the applied test temperature and loading cycle.

Toughening Mechanism for Ceramics by a Ductile Metallic Phase

The basic objective of this study is to establish the material design concepts for the coexistence of good high-temperature mechanical properties and super heat resistance in the systems of ceramic/metal and ceramic/ceramic functionally gradient materials (FGMs). Flexural and fracture toughness tests were conducted on gas-pressure combustion-sintered Cr 3 C 2 ceramic and its composites with Ni and TiC (Cr 3 C 2 /Ni, Cr 3 C 2 /TiC) in a vacuum environment up to 1 200°C using a newly developed materials testing system. Fracture characteristics were investigated on the basis of fracture mechanics and fractography. The toughness of Cr 3 C 2 can be improved by the addition of metallic particles. It is found that the principal mechanism of toughness improvement in these composites (ductile-phase reinforced ceramic matrix composites) is attributable to crack-tip plastic blunting by a ductile metallic phase.

Rate and temperature effects on crack blunting mechanisms in pure and modified epoxies

The failure mechanisms of several epoxy polymers (including pure, rubber- and particulatemodified, as well as rubber/particulate hybrid epoxies) were investigated over a wide range of strain rates (10−6 to 102 sec−1) and temperatures (−80 to 60° C). A substantial variation in fracture toughness, GIc, with rate was observed at both very high and very low strain rates. Under impact testing conditions, GIc for both pure and rubber-modified epoxies displayed peaks at about 23 and −80° C which appeared to correlate with the corresponding size of the crack tip plastic zone. In order to explain these rate and temperature-dependent GIc results, two separate crack blunting mechanisms were proposed: thermal blunting due to crack tip adiabatic heating and plastic blunting associated with shear yield/flow processes. Thermal blunting was found to occur in the pure- and rubber-modified epoxies under all impact testing conditions and temperatures above 0° C. For temperatures below −20° C under impact conditions, the fracture toughness is dependent on viscoelastic loss processes and not thermal blunting. Plastic blunting was predominant at very slow strain rates less than 10−2 sec−1 for the pure- and rubber-modified epoxies and at impact strain rates for the fibre and hybrid epoxies. Microstructural studies of fracture surfaces provided some essential support for the two proposed crack blunting mechanisms.

Ａｌ‐Ｚｎ‐Ｍｇ‐Ｃｕ系合金の破壊じん性値と不純物元素の関係

A relationship between fracture toughness or critical crack tip opening displacement (CTODc) and Fe- and Si-rich insoluble inclusions in 7000 type alloys was studied. The magnitude of crack tip plastic blunting or fracture toughness is determined by forming characteristic dimples just in advance of the stretched zone. The dimples on fracture surfaces are classified into two types of populations by scanning electron micrography and energy dispersion spectroscopy analysis. One population includes coarse dimples 10μm in average size associated with coarse in clusions containing Fe or Si. The other includes smaller dimples less than 1μm in diameter having Cr-rich dispersoid particles. The average size of coarse dimples is in good agreement with the average spacing of inclusions 1μm or more in size. The growing stretched zone never exceed the average spacing of these inclusions. The characteristic dimples effective to determine CTODc are formed by the inclusions containing Fe or Si.

Mechanics of fatigue crack propagation by crack-tip plastic blunting

The power relation between the fatigue crack propagation rate da/ dN and the J integral range ΔJ was obtained for OFHC copper, 0.04%C steel and stainless steel (Type 304). The physical meaning of the relation was investigated based on the observation of the crack opening behavior and fractography. The striations, whose spacing was equal to da/ dN , confirm crack-tip blunting as being an operating mechanism for crack growth. da/ dN was expressed as a power function of the crack-tip opening displacement (Δ CTOD), da/ dN = A(Δ CTOD) p , where p was larger than one. The major portion of Δ CTOD contributes to crack growth at high rates, while a considerable fraction of Δ CTOD occurs behind the crack tip at low rates. Δ CTOD is correlated to ΔJ divided by the yield strength σ' Y through the equation, Δ CTOD = B(ΔJ/σ Y′) q , where q is nearly equal to one for 0.04%C steel and is larger than one for copper. The variation of q with material was explained based on the observed distribution of the crack opening displacement. The final equation for fatigue crack growth is given as da/ d N = A · B p(ΔJ/σ Y′) pq. When the shape of the crack tip opening is geometrically similar, both p and q are one. For a general case, both are larger than one, yielding the exponent of the da/ dN-ΔJ relation deviating from 1 up to 2.3.

Relation between Crack Tip Plastic Blunting and J-Integral

On the fracture surface of a KIc specimen, there exists a critical stretched zone between the fatigue pre-crack and overload fracture regions. This width, SZWc, has been correlated with the critical values of various fracture mechanics parameters. On the other hand, a sub-critical stretched zone appears as the loading progresses. In this paper, the data of sub-critical stretched zone width, SZW, obtained by many researchers were summarized and the relation between SZW, as a measure of crack tip plastic blunting, and the J-integral was investigated.The followings are the summary of the results obtained.(1) The relation between SZW and J/σflow showed an apparent dependence on flow stress, σflow: there was a tendency for SZW to become smaller for the same value of J/σflow as σflow became smaller. S0, the following equation did not stand, SZW=C1J/σflow (C1: const.).(2) The change of Young's modulus, E, had little influence on the relation between SZW and J/E, and no influence of test temperature was observed. SZW was given by the following expression, SZW=89J/E(3) The above mentioned relation between SZW and J was similar to the one between the striation spacing, S, and J. Under a small scale yielding condition, S was given by the following expression, in the case that the stress ratio is 0, S=9.4J/EThat is to say, the width of the stretched zone as well as that of a striation formed by the same micromechanism of glide plane decohesion, was characterized by the very same fracture mechanics parameters.(4) If the above-mentioned relation between SZW and J is established on other materials, there is a possibility of evaluating JIc simply by measuring SZWc with a single specimen by failured overload.

A quantitative stereoscopic fractographic study of the mechanism of fatigue crack propagation in nickel

Continuous profiles of the mating fatigue fracture surfaces in polycrystalline nickel of high purity (99.999% Ni) were studied by stereoscopic electron fractography method. Fatigue striation features were examined and a direct proof of the hill-to-depression matching of the opposite mating fracture surfaces was obtained. The narrow, much deformed sides of fatigue striations on the opposite surfaces face one another and are shown to be the area of contact of the opposite mating fatigue striations. A new mechanism of fatigue crack propagation is proposed, according to which the crack propagation within a load cycle consists of two phases: the phase of transverse shear crack propagation and the crack tip plastic blunting phase. Within the framework of the proposed model the explanation was given to various effects and, in particular, to the fact that the ratio of fatigue striation depth to its width decreases with the loading amplitude growth, as well as to the effects observed during program loading of the specimen.