Effect of a hard artificial asperity on the crack closure behavior in an annealed SAE 1015 steel

The load-crack opening displacement (COD) curves and deformation characteristics in the vicinity of a hard artificial asperity in an annealed SAE 1015 steel were studied. The artificial asperity was found to have a significant effect on the trend of the load-COD curves. The lower portion of the load-COD curves in the unloading phase exhibited a convex shape without the asperity, but a concave shape with the asperity. The concave shape, signifying the acceleration in the COD decrease, was further verified by varying the size of the asperity, conducting special compression tests and elastic-plastic load-COD tests. The plastic deformation in the vicinity of both asperity and crack tip was studied via microhardness tests, etching techniques, and finite element analysis. Based on the experimental observations, a modified crack closure process model was proposed, where three stages of the unloading curve was defined: (i) the asperity does not contact the upper crack face, (ii) a process where both the asperity and the specimen material deform elastically, and the elastic-wedge model is applicable, and (iii) the plastic deformation of the specimen material adjacent to the asperity occurs, thus resulting in the concavely shaped load-COD curves. An equation was proposed to estimate the COD values, in which the plastic deformation both at the crack tip and at the asperity was considered. The residual COD calculated from the proposed equation was found to be consistent with the experimental results.     

Crack closure under high load-ratio conditions for Inconel-718 near threshold behavior

Fatigue-crack-growth (FCG) rate tests were conducted on compact specimens made of an Inconel-718 alloy to study the behavior over a wide range in load ratios (0.1 ? R ? 0.95) and a constant K_max test condition. Previous research had indicated that high R (>0.7) and constant K_max test conditions near threshold conditions were suspected to be crack-closure-free and that any differences were attributed to K_max effects. During a test at a load ratio of 0.7, strain gages were placed near and ahead of the crack tip to measure crack-opening loads from local load-strain records during crack growth. In addition, a back-face strain (BFS) gage was also used to monitor crack lengths and to measure crack-opening loads from remote load-strain records during the same test. The BFS gage indicated that the crack was fully open (no crack closure), but the local load-strain records indicated significant amounts of crack closure. The crack-opening loads were increasing as the crack approached threshold conditions at R = 0.7. Based on these measurements, crack-closure-free FCG data (ΔK_eff against rate) were calculated. The ΔK_eff-rate data fell at lower ΔK values and higher rates than the constant K_max test results. In addition, constant R tests at extremely high R (0.9 and 0.95) were also performed and compared with the constant K_max test results. The constant R test results at 0.95 agreed well with the ΔK_eff-rate data, while the R = 0.9 data agreed well with constant K_max test data in the low-rate regime. These results imply that the R = 0.7 test had a significant amount of crack closure as the threshold was approached, while the R = 0.9 and K_max test results may have had a small amount of crack closure, and may not be closure free, as originally suspected. Under the high load-ratio conditions (R ? 0.7), it is suspected that the crack surfaces are developing debris-induced crack closure from contacting surfaces, which corresponded to darkening of the fatigue surfaces in the near-threshold regime. Tests at low R also showed darkening of the fatigue surfaces only in the near-threshold regime. These results suggest that the ΔK_eff against rate relation may be nearly a unique function over a wide range of R in the threshold regime.     

Analytical and numerical study of cohesive zones for a crack in an adhesive layer between identical isotropic materials

A crack in a thin adhesive elastic-perfectly plastic layer between two identical isotropic elastic half-spaces is considered. Uniformly distributed normal stress is applied to the substrates at infinity. First, stress distribution in the cohesive zones and the J-integral values are defined numerically by the finite element method (FEM). Further, a mathematical formulation of the problem is given and its analytical solution is proposed. It is assumed that, at the crack continuations, there exist cohesive zones. The interlayer thickness is neglected since it is much smaller than the crack length. The distribution of the normal stress, which was obtained by means of the FEM, is now approximated by a piecewise-constant function and assumed to be applied at the faces of the cohesive zones. The formulated problem is solved analytically and an equation for determination of the cohesive zone lengths is derived. Also, closed expressions for the crack tip opening displacement and for the J-integral are obtained in an analytical form. These parameters are found with respect to the values of the normal stress applied at infinity. Finally, a universal approximating function, which describes the stress distribution in the cohesive zones, is constructed. This function depends on the ratio between the interlayer thickness and the crack length and on the ratio between the normal stress applied at infinity and the yield limit of the interlayer’s material. Once again, the problem is solved analytically, but this time for the stress distribution prescribed by the universal approximating function. The cohesive zone lengths, the values of the crack tip opening displacement and of the J-integral are calculated. A comparative analysis of the obtained results is carried out. A good agreement of the J-integral values calculated by means of the developed analytical models and by the associated finite element analysis is demonstrated.     

The jump-like crack growth model, the estimation of fracture energy and JR curve

In this paper the jump-like crack growth model for monotonic loading is applied to re-examine both the onset of crack growth and process of stable crack growth. In the former case the fracture energy associated with a new surface creation is estimated and the in-plane constraint influence on this quantity is examined using the J-A₂ approach. In the later case the formula to compute the J-resistance curve is re-examined and compared with the one known from the standards. In the analysis the plane strain model of a structural element made of elastic-plastic material is assumed.     

Crack-closure behavior of 2324-T39 aluminum alloy near-threshold conditions for high load ratio and constant Kmax tests

Fatigue-crack-growth rate tests were conducted on compact specimens made of 2324-T39 aluminum alloy to study the behavior over a wide range in load ratios (0.1  R  0.95) and a constant K_max test condition. Previous research had indicated that high R (> 0.7) and constant K_max test conditions near threshold were suspected to be crack-closure free and that any differences were attributed to K_max effects. During the tests, strain gages were placed near and ahead of the crack tip to measure crack-opening loads from local strain records on all tests, except R = 0.95. In addition, a back-face strain gage was used to monitor crack lengths and also to measure crack-opening loads from remote strain records. From local gages, significant amounts of crack closure were measured at the high-R conditions and crack-opening loads were increasing as the threshold condition was approached. Crack-closure-free data, ΔK_eff (= U ΔK) against rate, were calculated. These results suggest that the ΔK_eff against rate relation may be nearly a unique function over a wide range of R even in the threshold regime, if crack-opening loads were measured from local strain gages and not from remote gages. At low R, all three major shielding mechanisms (plasticity, roughness, and fretting debris) are suspected to cause crack closure. But at high R and K_max tests, roughness and fretting debris are suspected to cause crack closure above the minimum load.     

An investigation of crack closure and the propagation of semi-elliptical fatigue cracks in Q1N (HY80) pressure vessel steel

The results of an experimental investigation of the effect of crack closure on the propagation of semi-elliptical fatigue cracks are presented. Load-shedding fatigue threshold tests were carried out at stress ratios of 0.2, 0.35, 0.5 and 0.7. Crack closure was measured at the surface and depth positions using backface strain gauges, near-tip gauges, and a clip gauge. Differences between the surface and depth growth behaviour are explained by considerations of the effects of the transition from plane stress conditions at the surface to plane strain conditions at the depth. The effects of stress ratios are attributed largely to differences in the crack opening displacement, which result in asperities coming into contact to induce roughness-induced crack closure.     

Analysis of vacuum fatigue crack growth results and its implications

Conventionally, the reduction of ΔK_th with load ratio R has been interpreted in terms of crack closure arising from plasticity, oxide or crack surface roughness. Since, plane-strain conditions exist near-threshold, plasticity-induced closure is absent. Therefore, to account for R-ratio effects near-threshold, the oxide and roughness closure mechanisms have been proposed. Further analysis has shown that these other two closure effects also are small, when the results taken in vacuum were included. The present analysis shows that there is a unique relation of the oxide thickness with a threshold K_max, rather than with a threshold ΔK. This threshold K_max (K*_max,th) depends on environment. When the applied K_max<K*_max,th, the crack is stationary in the presence of the oxide formation and grows only when the applied K_max>K*_max,th. Thus, the oxide thickness—K_max relation seems to have a bearing on the criterion for crack growth in the presence of the environment. Oxide formation passivates the crack surfaces and retards the environmental damage ahead of the crack-tip. Examples from CrMo and NiCrMo steels support this viewpoint and suggest that there is a pressing need for quantifying the crack-tip environmental effects and fatigue thresholds.     

Fractal modeling of the J-R curve and the influence of the rugged crack growth on the stable elastic-plastic fracture mechanics

In this paper, fractal geometry is used to modify the Griffith-Irwin-Orowan classical energy balance. Crack fractal geometry is introduced in the elastic-plastic fracture mechanics by means of the Eshelby-Rice J-integral and the influence of the ruggedness of the crack surface on the quasistatic crack growth is evaluated. It is shown that the rising of the J-R curve correlates to the topological ruggedness dimension of the crack surface. Results from fracture experiments are shown to be very well fitted with the proposed model, which is shown to be a unifying approach for fractal models currently used in fracture mechanics.     

Effects of component size, geometry, microstructure and aging on the embrittling behavior of creep crack growth correlated by the Q parameter

The driving force for creep crack growth is dominated by local elastic-plastic stress in the creep damage zone around a crack tip, temperature and microstructure. In previous work, C^∗, C_t, load line displacement rate dδ/dt and Q^∗ parameters have been proposed as formulations of creep crack growth rate (CCGR). Furthermore, using parameters mentioned above, the construction of the algorithm of predictive law for creep crack growth life is necessary for life assessment procedures. The aim of this paper is to identify the effects of component size, geometry, microstructure, aging and weldment on the embrittling behavior of creep crack growth and incorporate these effects in a predictive law, using the Q^∗ parameter. It was found that for specimen size (width and thickness) and of material softening due to aging the values of the activation energy were the same whereas for grain size change and structural brittleness, which affected crack tip multi-axial stress state the values for the activation energy for CCGR differ.     

Theoretical and numerical modelling of creep crack growth in a carbon-manganese steel

This paper presents an analytical and numerical study of time dependent crack growth at elevated temperatures. A triaxiality dependent damage model is used to represent the multiaxial creep ductility of the material and an analytical model to predict steady state crack growth in terms of the fracture parameter C^∗, designated the NSW-MOD model, is presented. This model is an enhancement of the earlier NSW model for creep crack growth as it accounts for the dependence of stress and strain on angular position around the crack tip. Elastic-creep and elastic-plastic-creep finite element analyses are performed for a cracked compact tension specimen and the crack propagation rate in the specimen is predicted. It is found that in general the NSW-MOD model gives an accurate estimate of the crack growth rate when compared to the finite element predictions and experimental data for a carbon-manganese steel. However, crack growth rates predicted from the finite element analysis at low values of C^∗ may be higher than those predicted by either the NSW or NSW-MOD model. This enhanced level of crack growth may be associated with the non-steady state conditions experienced at the crack tip.     

Experimental T33-stress formulation of test specimen thickness effect on fracture toughness in the transition temperature region

This paper describes a study of the test specimen thickness effect on fracture toughness of a material, in the transition temperature region, for CT specimens. In addition we studied the specimen thickness effect on the T₃₃-stress (the out-of-plane non-singular term in the series of elastic crack-tip stress fields), expecting that T₃₃-stress affected the crack-tip triaxiality and thus constraint in the out-of-plane direction. Finally, an experimental expression for the thickness effect on the fracture toughness using T₃₃-stress is proposed for 0.55% carbon steel S55C. In addition to the fact that T₃₃ (which was negative) seemed to show an upper bound for large B/W, these results indicate the possibility of improving the existing methods for correlating fracture toughness obtained by test specimen with the toughness of actual cracks found in the structure, using T₃₃-stress.     

An analysis of synergistic and antagonistic behavior during BTEX removal in batch system using response surface methodology

The removal of benzene, toluene, ethylbenzene and xylene (BTEX) as quaternary mixtures were studied in batch systems using a well-defined mixed microbial culture. The synergistic and antagonistic effects of total BTEX removal (BTEXT-RE) due to the presence of mixed substrate was evaluated through experiments designed by response surface methodology (RSM). The low and high concentrations of individual BTEX were 15 and 75 mg l(-1), respectively. The results showed that, increasing the concentration of xylene increased the cumulative BTEX removal (BTEXT-RE), however the reverse occurred when benzene concentrations were increased from low to high levels. A mixed response of increasing and decreasing trend in the BTEXT-RE value was observed when either of toluene or ethylbenzene concentration was increased. When the concentrations of individual BTEX compounds were 30 mg l(-1), the BTEXT-RE was about 58%. Complete BTEXT-RE was achieved at optimal BTEX concentrations of 48.1, 45.6, 49.3 and 56.6 mg l(-1). The RSM approach was found efficient in explaining the main, squared and interaction effects among individual BTEX concentrations on the BTEXT-RE in a more statistically meaningful way.     

Comparison of creep crack growth rate in heat affected zone of welded joint for 9%Cr ferritic heat resistant steel based on C, dδ/dt, K and Q parameters

Creep crack growth behavior is very sensitive to the materials’ micro-structures such as the heat affected zone of a weld joint. This is a main issue to be clarified for 9%Cr ferritic heat resistant steel for their application in structural components. In this paper, high temperature creep crack growth tests were conducted on CT specimens with cracks in the heat affected zone of weld joints of W added 9%Cr ferritic heat resistant steel, ASME grade P92. The creep crack growth behavior in the heat affected zone of welded joint was investigated using the Q^∗ concept following which the algorithm of predicting the life of creep crack growth has been proposed. Furthermore, three-dimensional elastic-plastic creep FEM analyses were conducted and the effect of stress multiaxiality of welded joint on creep crack growth rate was discussed as compared with that of base metal.     

Comparative study on the properties of amorphous carbon layers deposited from 1-hexene and propylene for dry etch hard mask application in semiconductor device manufacturing

Amorphous carbon layers (ACLs) were prepared by plasma enhanced chemical vapor deposition (PECVD) from 1-hexene (C₆H₁₂) and propylene (C₃H₆) as a carbon source at different temperatures for dry etch hard mask of semiconductor devices manufacturing process. The deposition rate of ACL deposited at 550 °C from C₆H₁₂ and C₃H₆ was 5050 Å/min and 6360 Å/min. Although the deposition rate of ACL deposited from C₆H₆ was lower than that from C₃H₆, normalized deposition rate of ACL deposited from C₆H₁₂ was 1.64 times higher than that from C₃H₆. The relative amount of hydrocarbon contents measured by FTIR (Fourier transformation infrared) and TDS (thermal desorption spectroscopy) was decreased with the increase of deposition temperature. Raman results showed that the numbers and size of graphite cluster of ACLs deposited from each source were increased with the increase of deposition temperature. The extinction coefficient of ACL deposited at 550 °C from C₆H₁₂ was 0.51 and that from C₃H₆ was 0.48. The density of ACL deposited at 550 °C from C₆H₁₂ was 1.48 g/cm³ and that from C₃H₆ was 1.45 g/cm³. The dry etching rate of ACL deposited at 550 °C from C₆H₁₂ was 1770 Å/min and that from C₃H₆ was 1840 Å/min. The deposition rate, dry etch rate and the amount of hydrocarbon contents of ACLs deposited from each carbon source were decreased with the increase of deposition temperature but extinction coefficient and density were increased with the increase of deposition temperature. We concluded that the variation behavior of the deposition characteristics and film properties of ACLs from C₆H₁₂ with the increase of deposition temperature was the same as those of ACLs from C₃H₆. The high density and low dry etch rate of ACL from C₆H₁₂ can be explained by less hydrocarbon incorporation during deposition and these properties are more favorable for the dry etch hard mask application in semiconductor device fabrication.     

Effects of various environments on fatigue crack growth in Laser formed and IM Ti–6Al–4V alloys

The fatigue crack growth behaviors of Laser formed and ingot metallurgy (IM) Ti–6Al–4V alloys were studied in three environments: vacuum, air and 3.5% NaCl solution. Taking the Unified Fatigue Damage Approach, the fatigue crack growth data were analyzed with two intrinsic parameters, stress intensity amplitude ΔK and maximum stress intensity K_max, and their limiting values ΔK^* and . Fatigue crack growth rates da/dN were found increase with stress ratio R, highest in 3.5% NaCl solution, somewhat less in air and lowest in vacuum, and higher in IM alloy than in Laser formed one. In 3.5% NaCl solution, stress corrosion cracking (SCC) was superimposed on fatigue at R=0.9 for where K_max>K_ISCC, the threshold stress intensity for SCC. This and environment-assisted fatigue crack growth were evidenced by the deviation in fatigue crack growth trajectory (ΔK^* vs. curve) from the pure fatigue line where . Furthermore, the fractographic features, identified along the trajectory path, reflected the fatigue crack growth behaviors of both alloys in a given environment.