An Investigation of the Effects of Crack Front Curvature on the Crack-Tip Opening Displacement of A707 Steel

This paper examines the effects of crack front curvature on the fracture toughness (crack-tip opening displacement) of A707 steel. Fracture mechanics specimens, in which the radii of curvature of the crack fronts are controlled in an effort to simulate potential variations in crack front profiles in fracture experiments, were produced by machining and fatigue pre-cracking. Three-point bend crack-tip opening displacements (CTOD_c) were measured in accordance with the ASTM E-1290 code. The results show that the critical CTOD_c increases with increasing crack front curvatures between 0.05 and 0.17 mm^–1. In all cases, stable crack growth and final catastrophic failure of the specimens are found to occur by transgranular ductile dimpled fracture, in which the ductile dimples are nucleated around MnS or Al₂(Mg)O₃ inclusions. The implications of the results are discussed for the measurement of critical CTOD_c in specimens with varying levels of crack front curvature.     

A survey of failure criteria and parameters in mixed-mode fatigue crack growth

From the present survey of the mixed-mode crack growth criteria based on the fracture toughness K _Ic (critical J-integral), it follows that this concept is very extensively and variously used by different authors. The criteria discussed in the work are based on the parameters K, δ, W, and J. The most extensively applied models include the mixed mode I + II described by the stress intensity factor K. The criteria presented in the work are based on the factors affecting the fatigue crack growth during testing, namely stress, crack-tip displacement, or energy dissipation. In the case of mixed-mode cracking, special attention should be paid to the energy approach (application of the J-integral and strain energy density), which seems to be very promising for elastoplastic materials. Under mixed-mode cracking, two things should be taken into account: the rate and direction of fatigue-crack growth. Moreover, the nonproportional loading, crack closure, or overloads strongly affect the process of fatigue crack growth in the case of mixed-mode cracking.     

Prediction of fracture toughness for heat-resistant steels considering specimen dimensions. Report 2. Ductile fracture

A model of ductile failure of a body with a crack has been developed which enables predicting fracture toughness on the upper shelf of the fracture toughness temperature dependence taking into account the influence of the stress state. The model is based on the physical-mechanical model of ductile failure which is controlled by the critical value εf reached by plastic strain at the crack tip ε _i ^ρ . In this case it is assumed that both the ε _i ^ρ value, which precedes the crack growth onset by the mechanism of pore coalescence, and the critical strain εf are functions of specific stress state parameters, namely: the critical strain is a function of the stress state triaxiality σ _m /σ _n (σ _m is the hydrostatic stress, σ _i is the stress intensity), and ε _i ^ρ is a function of the parameter χ introduced, which is an explicit function of all three principal local stresses in the process zone at the crack tip and which defines the degree to which the stress state approaches the plane strain conditions for a body of specified thickness. The model developed has two modifications one of which enables predicting fracture toughness of large-size bodies from the results of testing only small cylindrical specimens without cracks (smooth and with a circular recess) and the other from the results of testing small cylindrical specimens and small specimens with a crack. Translated from Problemy Prochnosti, No. 2, pp. 5–19, March–April, 1997.     

On the constancy of the specific enthalpy of fracture

The specific enthalpy of fracture due to ductile crack propagation in commercial polycarbonate sheet is calculated as ^* =A _1c/R _1c, whereA _1c is the critical energy release rate associated with the onset of unstable crack propagation andR _1c is the corresponding amount of damage (yielded material) formed per unit crack extension.A _1c andR _1c are determined from fatigue crack propagation experiments conducted at different maximum loads, load ratios and frequencies. The value of ^* obtained from all experiments is found to be 9.8±1.4 cal g^–1 (1cal = 4.184 J) which indicates that ^* is a material constant. This finding substantiates predictions of the crack layer theory.     

Modeling the brittle–ductile transition in ferritic steels: dislocation simulations

We present a model for the brittle–ductile transition in ferritic steels based on two dimensional discrete dislocation simulations of crack-tip plasticity. The sum of elastic fields of the crack and the emitted dislocations defines an elasto–plastic crack field. Effects of crack-tip blunting of the macrocrack are included in the simulations. The plastic zone characteristics are found to be in agreement with continuum models, with the added advantage that the hardening behavior comes out naturally in our model. The present model is composed of a macrocrack with microcracks ahead of it in its crack-plane. These microcracks represent potential fracture sites at internal inhomogeneities, such as brittle precipitates. Dislocations that are emitted from the crack-tip account for plasticity. When the tensile stress along the crack plane attains a critical value σ _F over a distance fracture is assumed to take place. The brittle–ductile transition curve is obtained by determining the fracture toughness at various temperatures. Factors that contribute to the sharp upturn in fracture toughness with increasing temperature are found to be: the increase in dislocations mobility, and the decrease in tensile stress ahead of the macrocrack tip due to increase in blunting, and the slight increase in fracture stress of microcracks due to increase in plasticity at the microcrack. The model not only predicts the sharp increase in fracture toughness near the brittle–ductile transition temperature but also predicts the limiting temperature above which valid fracture toughness values cannot be estimated; which should correspond to the ductile regime. The obtained results are in reasonable agreement when compared with the existing experimental data.     

An analysis of the brittle to ductile transition in polycrystalline ice under tension

Concepts of dislocation micromechanics and of fracture mechanics have been used to derive a quantitative criterion for the brittle/ductile transition in polycrystalline ice under tension. The criterion is written in terms of a critical grain size d_c, which is expressed as a function of both environmental parameters (temperature, strain rate) and material parameters (fracture toughness, lattice resistance to dislocation glide, grain boundary resistance to the propagation of slip). For d > d_c the ice is considered to be brittle; for d < d_c, it is ductile. While detailed experiments are needed to test the analysis, comparisons show reasonable agreement between theory and the limited data available.     

Simulation of dynamic crack growth using the generalized interpolation material point (GIMP) method

Dynamic crack growth is simulated by implementing a cohesive zone model in the generalized interpolation material point (GIMP) method. Multiple velocity fields are used in GIMP to enable handling of discrete discontinuity on either side of the interface. Multilevel refinement is adopted in the region around the crack-tip to resolve higher strain gradients. Numerical simulations of crack growth in a homogeneous elastic solid under mode-II plane strain conditions are conducted with the crack propagating along a weak interface. A parametric study is conducted with respect to varying impact speeds ranging from 5 m/s to 60 m/s and cohesive strengths from 4 to 35 MPa. Numerical results are compared qualitatively with the dynamic fracture experiments of Rosakis et al. [(1999) Science 284:1337–1340]. The simulations are capable of handling crack growth with crack-tip velocities in both sub-Rayleigh and intersonic regimes. Crack initiation and propagation are the natural outcome of the simulations incorporating the cohesive zone model. For various impact speeds, the sustained crack-tip velocity falls either in the sub-Rayleigh regime or in the region between (c _S is the shear wave speed) and c _D (c _D is the dilatational wave speed) of the bulk material. The Burridge–Andrews mechanism for transition of the crack-tip velocity from sub-Rayleigh to intersonic speed of the bulk material is observed for impact speeds ranging from 9.5 to 60 m/s (for normal and shear cohesive strengths of 24 MPa). Within the intersonic regime, sustained crack-tip velocities between 1.66 c _S (or 0.82 c _D ) and 1.94 c _S (or 0.95 c _D ) were obtained. For the cases simulated in this work, within the stable intersonic regime, the lowest intersonic crack-tip velocity obtained was 1.66 c _S (or 0.82 c _D ).     

Methods for the construction of the diagrams of fatigue crack-growth rate of materials

We study different parameters used for the construction of the diagrams of fatigue crack-growth rate of materials in the force, deformation, and energy approaches and tested for 08kp low-strength steel and 60 high-strength steel. The applicability of the dependences known from the literature for the evaluation of the crack-tip opening displacement and local strain energy at the crack tip is analyzed. It is shown that the range of local strains Δε* and the total range of dissipation of local energy in a loading cycle ΔW _t * specify the fatigue crack-growth rate in the material and that the da / dN−Δε* and da / dN−ΔW _t * diagrams are more sensitive to the structural and mechanical characteristics of the materials than the ordinary da / dN−ΔK diagrams. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 43, No. 4, pp. 31–41, July–August, 2007.     

Notch ductile failure with significant strain‐hardening: The modified equivalent material concept

The equivalent material concept (EMC) assumes that the ductile material has a valid K‐based fracture toughness (K_Ic or K_c). For ductile materials with significant strain‐hardening, no valid K_Ic or K_c is determined by the standard experiments and, hence, EMC seems null. The modified EMC (MEMC) is proposed in this study by which a virtual K_c value is defined and computed for the ductile material with significant strain‐hardening. In this way, Mode I and mixed Mode I/II fracture behaviors of U‐notched aluminum alloy 5083 are assessed in the view points of experiments and theories. Several U‐notched rectangular samples are used for performing the experiments and obtaining the failure loads. Then, the MEMC is coupled with the maximum tangential stress and mean stress criteria and utilized to predict the failure loads theoretically. Finally, it is shown that both the MEMC‐stress‐based criteria can provide very good predictions of the test data.     

Crack velocity dependence of longitudinal fracture in bone

An evaluation of the fracture characteristics of bovine tibia compact tension specimens associated with controlled crack propagation in the longitudinal direction has been made. The fracture mechanics parameters of critical strain energy release rate (G _c) and critical stress intensity factor (K _c) were determined for a range of crack velocities. A comparative fracture energy (W) was also evaluated from the area under the load-deflection curve. It was found that an increase in the average crack velocity from 1.75 to 23.6×10^–5 m sec^–1 produced increases in G _c (from 1736 to 2796 J m^–2), K _c (from 4.46 to 5.38 MN m^–3/2) and W. At crack velocities >23.6×10^–5 m sec^–1, W decreased appreciably. Microstructural observations indicated that, for crack velocities <23.6 m sec^–1, relatively rough fracture surfaces were produced by the passage of the crack around intersecting osteons (or lamellae), together with some osteon pull-out. In contrast, at a higher crack velocity, fracture was characterized by relatively smooth surfaces, as the crack moved indiscriminately through the microstructural constituents.     

A framework to correlate a/W ratio effects on elastic-plastic fracture toughness (J c )

Single edge-notched bend (SENB) specimens containing shallow cracks (a/W < 0.2) are commonly employed for fracture testing of ferritic materials in the lower-transition region where extensive plasticity (but no significant ductile crack growth) precedes unstable fracture. Critical J-values J _c ) for shallow crack specimens are significantly larger (factor of 2–3) than the J _c )-values for corresponding deep crack specimens at identical temperatures. The increase of fracture toughness arises from the loss of constraint that occurs when the gross plastic zones of bending impinge on the otherwise autonomous crack-tip plastic zones. Consequently, SENB specimens with small and large a/W ratios loaded to the same J-value have markedly different crack-tip stresses under large-scale plasticity. Detailed, plane-strain finite-element analyses and a local stress-based criterion for cleavage fracture are combined to establish specimen size requirements (deformation limits) for testing in the transition region which assure a single parameter characterization of the crack-tip stress field. Moreover, these analyses provide a framework to correlate J _c )-values with a/W ratio once the deformation limits are exceeded. The correlation procedure is shown to remove the geometry dependence of fracture toughness values for an A36 steel in the transition region across a/W ratios and to reduce the scatter of toughness values for nominally identical specimens.     

Limiting Equilibrium of a Cracked Body with Regard for the Specific Features of the Distribution of Stresses Near the Crack Tip

By using the well-known δ _c -model, we establish new formulas for the evaluation of the crack-tip opening displacement with regard for a more complicated interaction of the edges of a model cut in the process zone of the material and determine the dependence of the critical load on the ratio of the initial crack length to the length of the process zone regarded as constant. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 41, No. 4, pp. 5–8, July–August, 2005.     

Van der Waals chain-molecule fluid in self-consistent field approximation: Some thermal properties

The van der Waals equation for a monomer is used to derive the equation of state for a fluid consisting of chain molecules of equal length. The evolution of a part of the diagram of state pertaining to liquid-vapor equilibrium is treated for the case of an increase in the number of links in a molecule. The dependences on the number of links n are found for the following properties of polymer fluid: the critical temperatureT _c , the critical pressurep _c , the critical density p_c, the critical compressibilityz _c , the temperature of normal boiling, the Riedel parameter of similarity a, the acentric factor Ω, and the enthalpy of vapor formation δH_V, A comparison with the experimental data forn-alkanes and 1-alkanols reveals that the obtained dependences reflect qualitatively correctly the variation of the above-identified properties with an increase of the number of links in a molecule. For long chains(n ≪ 1), the scaling dependences are determined for the properties of a chain-molecule fluid:T _c ∽n ^−1/2,p _c ∽n ^−3/2ρ_c∽n ^−1/2,z _c∽n ⁻¹,α∽n, ω∽n ^2/3,ΔH _ν∽n.     

Rate-dependent fracture toughness of pure polycrystalline ice

A series of three-point bend tests using single edge notched testpieces of pure polycrystalline ice have been performed at three different temperatures (–20°C, –30°C and –40°C). The displacement rate was varied from 1 mm/min to 100 mm/min, producing the crack tip strain rates from about 10^–3 to 10^–1 s^–1. The results show that (a) the fracture toughness of pure polycrystalline ice given by the critical stress intensity factor (K _IC) is much lower than that measured from the J—integral under identical conditions; (b) from the determination of K _IC, the fracture toughness of pure polycrystalline ice decreases with increasing strain rate and there is good power law relationship between them; (c) from the measurement of the J—integral, a different tendency was appeared: when the crack tip strain rate exceeds a critical value of 6 × 10^–3 s^–1, the fracture toughness is almost constant but when the crack tip strain rate is less than this value, the fracture toughness increases with decreasing crack tip strain rate. Re-examination of the mechanisms of rate-dependent fracture toughness of pure polycrystalline ice shows that the effect of strain rate is related not only to the blunting of crack tips due to plasticity, creep and stress relaxation but also to the nucleation and growth of microcracks in the specimen.     

A theory-based method for correlation and prediction of dense-fluid transport properties

Dense-fluid transport property data for a wide range of compounds have been successfully correlated on the basis of universal curves for the reduced diffusion coefficient,D ^*, the reduced viscosity, η^* and the reduced thermal conductivity, λ^*, against the reduced volumeV/V _o , whereV is the molar volume, andV _o is a characteristic volume equal to the volume of close packing for a system of hard spheres. The reduced transport properties,X ^*, are defined in terms of the low-density hard-sphere values by (X/X _o )(V/V _o )^2–3, whereX is ν, λ, or the product of the number density and the diffusion coefficient. To provide a theoretical justification for this approach, extensive computer simulation results for these transport properties, given in the literature for a system of Lennard-Jones (12–6) molecules, have been considered. It is found that the reduced transport properties for different temperatures are superimposable upon the results for any reference isotherm when plotted versus logV, as found previously for real fluids. However, to reproduce this density dependence at any given temperature on the basis of the universal curves, the characteristic volume for self-diffusion must be greater than that for viscosity or thermal conductivity. Invited paper presented at the Fourth Asian Thermophysical Properties Conference, September 5–8, 1995, Tokyo, Japan.     

Crack significance evaluation with special reference to welded structures

Fracture mechanics parameters (stress intensity factorK _I and its critical valueK _Ic , crack opening displacement, and the contourJ integral) are originally defined for static and quasistatic loading conditions. On the basis of theoretical background, standard test methods for the experimental determination of their specific values were developed. Structural integrity analysis requires the extension of application of these parameters to other types of loading. We propose new parameters for stress corrosion (stress corrosion cracking thresholdK _1sco ), for cyclic loading (stress intensity factor range ΔK and fatigue threshold ΔK _th), and for creeping at elevated temperatures (C ^* andC _t integrals). The structural integrity of welded structures is mainly affected by cracks in welded joints. We demonstrate the practical application of fracture mechanics parameters to the evaluation of structural integrity under the above-mentioned loading conditions. Faculty of Technology and Metallurgy, University of Belgrade, Yugoslavia. Faculty of Mechanical Engineering, University of Belgrade, Yugoslavia. Published in Fizyko-Khimichna Mekhanika Materialiv, Vol. 32, No. 2, pp. 107–118, March–April, 1996.     

Further studies on the characteristics of the T * ɛ integral: Plane stress stable crack propagation in ductile materials

Some Characteristic behavior of the T ^* _ɛ (Atluri, Nishioka and Nakagaki (1984)) is identified in this paper through an extensive numerical study. T ^* _ɛ is a near tip contour integral and has been known to measure the magnitude of singular deformation field at crack tip for arbitrary material models. In this paper, T ^* _ɛ is found to behave quite differently for different choices of near tip integral contours. If the integral contour moves with advancing crack tip (moving contour), then T ^* _ɛ measures primarily the energy release rate at the crack tip. It is very small for metallic materials, and tends to zero in the limit as Δa→0 for low hardening materials. Thus, T ^* _ɛ evaluated on a moving contour tends to zero as ɛ→0 and Δa→0, for low hardening materials. If the integral contour elongates as crack extends (elongating contour), then T ^* _ɛ measures total energy inside the volume enclosed by Γ_ɛ [i.e., the energy dissipated in the extending wake] plus the energy release at the crack tip. Furthermore, the difference in the behavior of CTOA and T ^* _ɛ, when the applied load is slightly perturbed, is identified. The CTOA is found to be quite insensitive to applied load change. T ^* _ɛ is found to be roughly proportional to the square of the applied load. The functional shape of T ^* _ɛ in terms of the size ɛ of integral contour (for the elongating contour case), is identified, using the crack tip asymptotic formula of Rice (1982). Also, the behaviors of CTOA and T ^* _ɛ are discussed from the view point of Rice's asymptotic solution. It is recommended that as a crack tip parameter for ductile materials, T ^* _ɛ with elongating path be used. CTOA is sometimes not very sensitive to the applied load change, therefore it may create some numerical problems in application phase crack propagation analysis.     

Structure and properties of polyethyleneterephthalate crystallized by annealing in the highly oriented state

The structure of polyethyleneterephthalate bristles drawn about five times in the amorphous state and subsequently crystallized at temperatures between 100 and 260‡ C has been studied by means of small-angle X-ray scattering. In addition density, heat of fusion and wide-angle scattering behaviour were measured. For comparison, similar experiments were carried out with undrawn samples. The results showed that the degree of crystallinity of PET cannot be calculated from density data on the basis of a simple two-phase model, since the effective densitiesρ _c ^* andρ _a ^* of the crystalline and amorphous regions depend strongly on crystallization and drawing conditions. With rising crystallization temperature the size of the mosaic blocks building up the crystalline layers and their longitudinal mutual order increase whereas the volume fraction of the crystalline region is only rather slightly effected by the annealing temperature. The difference between the effective densityρ _c ^* and the “X-ray density”ρ _c of the crystalline layers is supposed to be caused by lattice vacancies in the boundaries of the mosaic blocks.     

Prediction of Ductile Fracture Toughness for Neutron-Irradiated Reactor Pressure-Vessel Steels. Part 2

The influence of neutron irradiation on the critical strain in tensile testing of smooth cylindrical specimens and on the local critical strain in ductile fracture of cracked specimens is simulated for 15Kh2MFA reactor pressure-vessel steel. Based on a series of calculations, we have developed an engineering scheme for estimating the irradiation-induced decrease in the upper-shelf level of the KI _c (T ) function.