Shallow-cracked Specimens Research Articles

Effect of Strain Hardening on the Estimation of J-Integral in Compact Tension Specimens

Compact tension (CT) specimen testing is used to compute the fracture toughness parameter J-integral for different materials using load-displacement curve. In this work, J is investigated for compact tension specimen for a strain-hardening material using plastic limit-load analysis. The hardening effect is accounted for through a simple linear hardening curve using a lower bound approach. Analytic expression for fracture parameters are derived from basic formulation. Results illustrated for different cases show that as the material strain hardening increases, the J-Integral increases especially for shallow crack specimens.

The effect of plastic constraint on the initiation of ductile tears in shipbuilding structural steels

In this paper, the effect of plastic constraint on the initiation of ductile tears in four different shipbuilding structural steels has been experimentally studied by measuring the J-integral and crack opening displacement COD at initiation in three-point bend specimens with deep and shallow notches. Experimental results of seven groups of different strength alloy steels show that both δi and Ji values of ductile tear from the shallow crack specimens which have less constraint flow field are significantly higher than those of deeply notched specimens. Slip-line-field analysis shows that, for shallow crack, the hydrostatic stress is lower than that from standard deeply cracked bend specimen, which develops a high level of crack tip constraint, provides a lower bound estimate of toughness, and will ensure an unduly conservative approach when applied to structural defects, especially if initiation values of COD and J-integral are used.

The prediction of constraint-dependent R6 failure assessment lines for a pressure vessel steel via micro-mechanical modelling of fracture

The work demonstrates the ability of micro-mechanical modelling (the local approach) to predict the effects of both temperature and crack tip constraint on the probability of cleavage failure and the anticipated amount of pre-cleavage tearing of a pressure vessel steel. The basic fracture toughness data comprised information from deep-cracked (high constraint) and shallow-cracked (low constraint) specimens tested at temperatures ranging from −45 to 20 °C. The micro-mechanical modelling of ductile rupture employed a temperature-independent Gurson model, which was used in combination with a temperature-sensitive cleavage model to analyse the data in the transition regime. The cleavage parameters were tuned using a Monte-Carlo technique, which compared the outcome of the finite element models with a random set of data drawn from the statistical model of the basic experimental data. Application of the modified boundary layer formulation allowed analyses of the effects of both constraint and temperature on the amount of ductile tearing and the probability of cleavage failure to be undertaken. The results of these can easily be seen in the R6 diagram through constraint–modified failure assessment lines as set out in Appendix 14 of R6. In particular, by displaying the constraint corrections available for 0.2 mm ductile crack growth and 5% probability of cleavage failure, this paper demonstrates the enhancement of fracture resistance that can be obtained from low-constraint geometries.

Plastic η factor solutions of homogeneous and bi‐material SE(T) specimens for toughness and creep crack growth testing

Based on slip line field analysis and finite element analysis of elastic‐perfectly plastic materials, plastic η factor solutions for single edge‐cracked specimens in tension (SE(T)) with a wide range of crack lengths are proposed, both for homogeneous specimens and for bi‐material specimens with interface cracks. Moreover, two different plastic η factor solutions are given: one based on experimental load–load line displacement records, ηVLLp , and the other based on experimental load–crack mouth opening displacement (CMOD) records, ηCMODp . Comparison with existing finite element results shows good agreement. For deep cracks (a/w > ∼0.45), the ηVLLp solutions are insensitive to the strain hardening, to the specimen length and to the specimen thickness. However, for shallower cracks (a/w < ∼0.45), the ηVLLp solutions are sensitive to the specimen thickness, to the strain hardening and to the specimen length, suggesting difficulties associated with a robust determination of J and C * integrals from experimental data. On the other hand, the ηCMODp solution is not sensitive to the crack length, to the specimen thickness, to strain hardening and to the specimen length, even for shallow cracked specimens. This suggests that the use of CMOD can provide robust J and C * estimation schemes even for shallow crack testing.

Higher-order asymptotic crack-tip fields in a power-law creeping material

The higher-order asymptotic crack-tip fields are considered for a mode-I crack in a power-law creeping material under the plane strain conditions. Based on the three-term solution of Yang et al. (1993) and Chao et al. (1994) for hardening materials, this paper develops a three-term solution near a crack tip in creeping materials only with two parameters: C( t)-integral and a constraint parameter A 2( t). This solution is then discussed for conditions of small-scale creep, transient creep and extensive creep. In addition, detailed finite element analysis is performed for four specimens, namely, single-edge notched tension, three point bend, center-cracked panel and compact tension. Good agreement, in both angular and radial stresses, with finite element results confirms that the three-term asymptotic solution is universally valid for specimens possessing various crack-tip constraints and from small-scale creep to extensive creep. This statement is especially true for shallow cracked (or low constraint) specimens, where the dominant region for the HHR-type singularity does not practically exit.

Q-stresses and constraint behavior of the notched cylindrical tensile specimen

A non-linear numerical analysis of sharp-notched cylindrical specimens under tensile loading was performed, and Q-stresses for various crack lengths were derived at a load level equal to the limit load, P 0. Single-material specimens, representing the base metal of a welded joint, and bi-material specimens, representing an overmatched weld at the site of the crack, were modeled. The results show that shallow-cracked specimens behave as in a plane-stress condition, whereas deeply cracked specimens tend to behave in a plane-strain fashion. The presence of a portion of material (weld metal volume fraction=1/3) with different deformation properties has the effect of raising the constraint on the specimen. The limiting ratio of the diameter of the notch, d, to the outer specimen diameter, D, for a change in the constraint behavior of the notched cylindrical specimens, appears to be of the order of d/ D≈0.50.

J–R curves corrected by load-independent constraint parameter in ductile crack growth

The constraint effect on J–resistance curves of ductile crack growth is considered under the condition of two-parameter J–Q* controlled crack growth, where Q* is a modified parameter of Q in the J–Q theory. Both J and Q* are used to characterize the J–R curves with J as the loading level and Q* as a constraint parameter. It is shown that Q* is independent of applied loading under large-scale yielding or fully plastic deformation, and so Q* is a proper constraint parameter during crack growth. An approach to correct constraint effects on the J–R curve is developed, and a procedure of transferring the J–R curves determined from standard ASTM procedure to nonstandard specimens or real cracked structures is outlined.The test data of fracture toughness, JIC, and tearing modulus, TR, by Joyce and Link (Engng. Fract. Mech. 57(4) (1997) 431) for a single-edge notched bend specimen with various depth cracks are employed to demonstrate the efficiency of the present approach. The variation of JIC and TR with the constraint parameter Q* is obtained, and then a constraint-corrected J–R curve is constructed for the test material of HY80 steel. Comparisons show that the predicted J–R curves can match well with the experimental data for both deep and shallow cracked specimens over a reasonably large amount of crack extension.Finally, the present approach is applied to predict the J–R curves of ductile crack growth for five conventional fracture specimens. The results show that the effect of specimen geometry on the J–R curves is generally much larger than the effect of specimen sizes, and larger specimens tend to have lower crack growth resistance curves.

Experimental investigations on the ‘shallow crack effect’, on the 10 MnMoNi 5 5 steel, and computational analysis in the upper shelf by means of the global and local approaches

Shallow cracks have been of great interest for some years now, since it has been observed that standard fracture toughness parameters, determined on deep crack specimens, exhibit a geometrical dependence and that most of the structures containing cracks (in particular pressure vessels) exhibit crack depth to width ratios a/W much lower than fracture mechanics specimens tested in the laboratory. This study performed at MPA Stuttgart in collaboration with EDF, aimed first of all at investigating the ‘shallow crack effect’ on the high ductile, high strength, low strain-hardening shape welded 10 MnMoNi 5 5 steel over the whole temperature range of the transition region of toughness. Deep crack (CT25 and TPB25 with a/W=0.55) and shallow crack (TPB25 with a/W=0.066) specimens were tested, providing K IC, J i and J IC results. At the same time, computations were performed, in the upper shelf with, on the one hand, the usual elastic–plastic model (Von Mises model) and on the other hand, the local approach model of Rousselier. Experiments did not exhibit any shallow crack effect in the lower shelf (no increase in K IC) and show a slight effect in the transition region and in the upper shelf (slight increase in J i, larger increase in J IC). Computations confirmed the ability of the ‘modified’ Rousselier model to describe the macroscopical behaviour (F-CMOD curves) of the three types of specimens as well as to simulate their crack propagation behaviour (CMOD-Δ a curves). The combination of the Rousselier model with the line contour integral method enables us to develop the draft of an experimental method to determine the J-integral for any material and any initial crack length ( a/W remaining within 0.05 and 0.7), taking crack growth into account. This method, based on the measurement of the energy under the F-CMOD curve and an η c factor indexed on the current a/W ratio, provided an agreement within 10% and most of the time 5% between the experimental and computational J-integral results. Consequently, computations with the Rousselier model also correctly predicted the experimentally observed crack resistance curves, especially their geometrical dependence. The observation during crack growth of the triaxiality of the stress state in the first millimeters of the ligament enabled one to understand this geometrical dependence, high triaxiality accelerating crack growth leading to lower J–R curves. For shallow crack specimens, the crack tip being located close to the top surface, a stress relaxation occurs at this top surface leading to a loss of triaxiality at the crack tip and in the ligament, delaying crack growth and leading to higher crack resistance curves. Finally, the Rousselier model was found to confirm the experimentally observed J i values on the various tested specimens. Therefore, assuming that the Rousselier model can correctly describe initiation, computations with different stress–strain curves (different yield stress values and strain-hardening behaviours) were performed: it seems that the ‘shallow crack effect’ ( J i(shallow crack)/ J i(deep crack)) is controlled by strain-hardening independently of the yield stress, the absence of strain-hardening leading to the most important effect.

The two criteria diagram for creep crack initiation and its application to an ip-turbine

A two criteria diagram for creep crack initiation, proposed in 1984, is described. The diagram distinguishes between the two principal damage modes (ligament damage and crack tip damage) and is able to show also the influence of combinations of both modes on creep crack initiation. So it is possible to determine the initiation time of different shallow and deep cracked specimens regarding the loading situation at the crack tip and in the far field (ligament). TTie method was proven by a great number of creep crack initiation results from small scale and large scale specimens as well as of components. The diagram is applied to determine the creep crack initiation time for an intermediate pressure turbine—rotor with a fictitious crack like defect.

Influence of crack depth and strength matching on deformation and plastic zone for welded joint specimen

By using the 2-dimensional elasto-plastic finite element method, the effects of crack depth and strength matching properties of welds on the deformation and plastic zone have been studied for three point bend specimens. The results indicate that, in the loading process of a welded joint specimen, the influence of crack depth and strength matching properties on the deformation parameters such as loading point displacement, crack mouth opening displacement, plastic rotational factor, and development of plastic zone is evident. The boundary between shallow crack and deep crack specimens is also influenced by the strength matching of welded joints. Moreover, the crack depth and strength matching of the welded joints have an important effect on the fracture-resistant capability of the specimens. The fracture-resistant capabilities of shallow crack specimens and overmatched joint specimens are better than those of deep crack specimens and undermatched joint specimens, respectively.

Fully plastic crack-tip fields for plane strain shallow-cracked specimens under pure bending

Detailed finite element (PE) analyses are performed to study the effect of crack depth on crack-tip constraint at full yielding for pure bending of plane strain single-edge-cracked specimens. Analyses are based on small-strain formulations and perfect plasticity. The crack depth a/W ranges from 0.1 to 0.7, and the deformation is applied up to the limiting state of full plasticity where crack-tip stresses reach steady-state limiting values.

On fractography of shallow and deep HY-100 cracked bend specimens

The influence of shallow cracks on the fracture behavior of structural components has been studied extensively in recent years. Finite element analyses have indicated dramatic differences in the crack-tip stress states between shallow and deep cracked bend specimens. In this study, an experimental program was carried out to investigate the fracture behavior of HY-100 steel containing various initial flow depths. Four a/w ratios ranging from 0.05 to 0.5 were chosen for the notched three-point bend tests. Test results showed that higher fracture toughness values are associated with specimens having shorter surface cracks. Also, fractographic studies indicated that two sets of dimples are present for a/w = 0.5 specimen, one set of equiaxed dimple for a/w = 0.05 specimen near the crack initiation zone. As the crack grows, increases in the volume fraction of the small dimple were observed. Finally, it showed that the characteristic features of surfaces can be correlated with the previous numerical predictions.

The significance of crack depth in fracture toughness specimens for HSLA steel welds

This work deals with the influence of crack depth on the plastic rotation tractor ( r p ) and fracture toughness at crack initiation and maximum load. A series of tests was performed on high strength low alloyed (HSLA) steel welds, where the ratio of crack length to specimen width was about 0.05–0.5, keeping a/W constant, at room temperature and transition temperature. It is found that the r p is not a fixed value for both deep and shallow crack specimens during the loading process. At first the r p value increases from a threshold crack opening displacement (COD) value rapidly with increased crack opening, then the rising rate of r p decreases. Finally, r p tends toward a constant. At the transition temperature, much the same trend is expected, but there exists a large scatter of fracture toughness. Moreover, the threshold COD condition, in which r p is zero, is established. Three characteristic values of r p on the r p- COD curves are defined corresponding to the local and apparent crack initiation and maximum load toughness, respectively. The r p values at the initiation or maximum load are not sensitive to the crack depths and the mechanical properties of crack tip materials for the welded joints tested. In addition, it is indicated that there exist different rising rates with decreasing crack depths between the initiation toughness described by the crack tip opening displacement ( δ i ) and the J- integral ( J i ), and between the initiation ( δ i or J i ) and maximum load toughness ( δ m or J m ). Finally, the effect of mechanical heterogeneity on fracture toughness for specimens with shallow cracks has been considered.

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 Jc) for shallow crack specimens are significantly larger (factor of 2–3) than the Jc)-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 Jc)-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.

Effects of crack depth on elastic-plastic fracture toughness

Short crack test specimens (a/W ≪ 0.50) are frequently employed when conventional deep crack specimens are either inappropriate or impossible to obtain, for example, in testing of particular microstructures in weldments and in-service structures containing shallow surface flaws. Values of elastic-plastic fracture toughness, here characterized by the crack tip opening displacement (CTOD), are presented for square (cross-section) three-point bend specimens with a/W ratios of 0.15 and 0.50 throughout the lower-shelf and lower-transition regions. Three dimensional, finite-element analyses are employed to correlate the measured load and crack mouth opening displacement (CMOD) values to the corresponding CTOD values, thus eliminating a major source of experimental difficulty in previous studies of shallow crack specimens. In the lower-transition region, where extensive plasticity (but no ductile crack growth) precedes brittle fracture, critical CTOD values for short crack specimens are significantly larger (factor of 2–3) than the CTOD values for deep crack specimens at identical temperatures. Short crack specimens are shown to exhibit increased toughness at the initiation of ductile tearing and decreased brittle-to-ductile transition temperatures. Numerical analyses for the two a/W ratios reveal large differences in stress fields ahead of the crack tip at identical CTOD levels which verify the experimentally observed differences in critical CTOD values. Correlations of the predicted stresses with measured critical CTOD values demonstrate the limitations of single-parameter fracture mechanics (as currently developed) to characterize the response.

Plastic ?-factor (? p )

Slip line field solutions for several commonly used fracture mechanics specimens are summarized. From these solutions analytic expressions of the plastic η p factors are derived. These results are then compared with those η p factors obtained using the EPRI's finite element analyses for power law strain hardening materials in order to assess the extent to which they can be approximately applied in J-integral tests with these specimens containing both deep and shallow cracks. It appears that in the deep crack specimens the η p factors are approximately equal for all hardening materials implying that the η p factors derived from slip line field solutions are accurate enough for J-integral evaluation. In the shallow crack specimens, with the exception of the double-edge cracked panels and pure bend specimens, the η p factors do not agree very well and reasons for the discrepancies are discussed.