Numerical investigation on stable crack growth in plane stress

Large deformation finite element analysis has been carried out to investigate the stress-strain fields ahead of a growing crack for compact tension (a/W=0.5) and three-point bend (a/W=0.1 and 0.5) specimens under plane stress condition. The crack growth is controlled by the experimental J-integral resistance curves measured by Sun et al. The results indicate that the distributions of opening stress, equivalent stress and equivalent strain ahead of a growing crack are not sensitive to specimen geometry. For both stationary and growing cracks, similar distributions of opening stress and triaxiality can be found along the ligament. During stable crack growth, the crack- tip opening displacement (CTOD) resistance curve and the cohesive fracture energy in the fracture process zone are independent of specimen geometry and may be suitable criteria for characterizing stable crack growth in plane stress. This revised version was published online in August 2006 with corrections to the Cover Date.     

THE EFFECTS OF CRACK DEPTH ON THE J-INTEGRAL AND CTOD FRACTURE TOUGHNESS FOR WELDED BEND SPECIMENS

This work deals with the influence of crack depth on the fracture toughness at initiation of crack growth and the constraint factor in relationship between the J-integral and the crack tip opening displacement (CTOD). A series of tests were performed on high strength low alloyed HT80 steel welds, and the critical J-integral and CTOD were determined using the load versus load point displacement record from three-point bend specimens with 0.05 < a/W < 0.5. It was found that the fracture toughness for shallow cracks at the onset of crack growth was larger than that for deep cracks for the steel welds tested, but it is felt that there is no fixed relationship between these values in the welds tested. The constraint factor is also a function of crack depth, and values of the factor increase from 0.5 to 1.5 when a/W increases from about 0.05 to 0.5. The factors are not very sensitive to the crack tip materials (HAZ or weld metal) in the welds tested.     

载荷方向和焊缝余高对氩弧焊缝疲劳性能的影响

采用疲劳寿命测试和观测断口方法,研究焊接方向和焊缝余高对TC2钛合金氩弧焊缝疲劳性能的影响。结果表明:同种焊接方向,保留焊高试件的疲劳寿命低于去焊高试件;同种焊缝余高处理方式,斜焊试件的疲劳寿命高于直焊试件。去焊高试件于气孔缺陷处萌生裂纹,保留焊高试件疲劳裂纹起源于焊趾。裂纹扩展初期,裂纹均在焊缝内扩展,有明显的疲劳条带;扩展后期,斜焊试件裂纹穿过焊缝进入母材,存在典型的韧性疲劳条带。直焊试件疲劳瞬断区韧窝少而浅;斜焊试件在母材瞬断,韧窝多且密。     

SHORT CRACK PROPAGATION AND CLOSURE EFFECTS IN A508 STEEL

Abstract— Fatigue crack growth measurements are usually made on standard specimens containing long cracks (～10 mm) although in most practical situations, a large part of the fatigue life is spent with much shorter dimensions. The purpose of the present study is a comparison of crack growth behaviour for long cracks (～13–16 mm) in CT specimens and smaller ones (～0.3–0.5 mm) in four point bend specimens. Large effects are noticed indicating that, at a given stress intensity factor amplitude, the crack growth rate is significantly higher in specimens with short cracks. Mouth displacement measurements for both specimen configurations show that the crack closure phenomenon accounts for the observed effect. Crack closure is likely to be associated with fracture surface roughness as shown by partly machining the material left behind the crack tip in CT specimens.     

Evaluation of elastic fracture mechanics parameters for bend specimens

Existing solutions for stress intensity factor and mouth opening displacement of three-point bend specimens are shown to overestimate these quantities for shallow cracks by up to ±4.5 percent, because they do not account for the disturbance of the bending stress distribution by the concentrated force at the loading point. This error is far larger than the accuracy claimed by these solutions (0.2 to 0.5 percent).New expressions are therefore developed for stress intensity, crack mouth opening displacement and crack mouth open angle of single edge notched bend specimens loaded in three-point bending. As a reference, and to show the accuracy of the solutions, also the pure bending situation is treated. Rigorously derived asymptotic solutions are used for the shallow and deep crack limits, in order to prescribe both the proper limit values and gradients to the interpolation functions, of which the intermediate values are derived from refined finite element analyses.The crack mouth opening angle solutions are primarily intended to facilitate crack mouth opening measurement at other locations then the specimen surface, i.e. at an offset from the specimen surface as is the case when removable knife edges are applied. No solutions of the crack mouth opening angle of three-point bend specimens were available until now. For use with unloading compliance crack length measurement, also an inverse crack mouth opening relation is developed. This also includes crack mouth opening measurement at an offset from the specimen surface, which is lacking in presently available expressions of this kind.     

Fracture toughness of transverse cracks in graphite/epoxy laminates at cryogenic conditions

Stress singularity of a transverse crack normal to ply-interface in a composite laminate is investigated using analytical and finite element methods. Four-point bending tests were performed on single-notch bend specimens of graphite/epoxy laminates containing a transverse crack perpendicular to the ply-interface. The experimentally determined fracture loads were applied to the finite element model to estimate the fracture toughness. The procedures were repeated for specimens under cryogenic conditions. Although the fracture loads varied with specimen thickness, the critical stress intensity factor was constant for all the specimens indicating that the measured fracture toughness can be used to predict delamination initiation from transverse cracks. For a given crack length and laminate configuration, the fracture load at cryogenic temperature was significantly lower. The results indicate that fracture toughness does not change significantly at cryogenic temperatures, but the thermal stresses play a major role in fracture and initiation of delaminations from transverse cracks.     

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.     

Crack propagation in AlZnMgCu 0.5 during static loading

Fatigue cracked bend specimens of the age hardened aluminum alloy AlZnMgCu 0.5 were investigated in interrupted static load tests. The purpose of the work described in the present paper was to get some informations about the behaviour of cracks under static loads. The fractographic observations showed that crack propagation due to static loads can be divided into two stages, namely initial crack propagation by minute amounts during the blunting of the crack tip and crack propagation due to dimple formation. Both stages of crack propagation can be described quantitatively by simple models. In addition, the stress intensity at the onset of the second crack propagation stage and the plane strain crack toughness can be predicted quite accurately.     

Dynamic crack propagation in large steel specimens

Dynamic fracture experiments on crack initiation and crack growth in single edge bend specimens are performed. The impact velocity is in the range of 14 to 50 m/s and the specimen size is 320×75 mm with a thickness varying from 18 to 40 mm. The experiments are recorded by high speed photography.Two different steel qualities are investigated and their constitutive characterisation are obtained from uni-axial tension tests and shear tests with strain rates in the range 10⁻⁴ to 10³ s⁻¹ and tension tests at temperatures between −196 and 600°C.One of the materials exhibits a transition from a ductile dimple fracture to a brittle cleavage fracture as the loading velocity increases and as the specimen thickness increases. Scanning electron microscope fractographs show that the density of plastic bridges within cleavage ligaments decreases with increasing impact velocity and with increasing specimen thickness. It is also noted that the local crack propagation direction deflects from the global one in cleavage fracture areas with a high density of plastic bridges.The other material fails in a ductile mode in all the investigated cases.     

J c DETERMINATION FOR SHALLOW NOTCH WELDED BEND SPECIMENS

Abstract— Methods are presented for the determination of J from 3 point bend specimens having 0.1 ≤ a/W ≤ 0.5 using the load versus crack mouth opening displacement trace. It is intended that the procedure be used to determine J_c , J at unstable fracture in the brittle to ductile transition, from specimens and test procedures which conform to the CTOD test standard BS5762. Elastic-plastic finite element computations are used to demonstrate the adequacy of the proposed estimation procedures for J and to show that it is still possible to apply them to specimens containing welded joints. The problems of defining a centre of rotation for plastic deformation in shallow notched bend specimens are discussed.     

ZTC4（Ti-6Al-4V）铸造钛合金的室温低周疲劳行为

研究了ZTC4钛合金应变控制的室温低周疲劳行为,对循环应力-应变和应变疲劳寿命数据进行了分析,通过双对数线性回归处理,得出了Manson-Coffin处理模型的疲劳参数。结果表明：ZTC4钛合金总应变幅在0.6%～0.8%时,材料存在轻度循环软化的现象;总应变幅为0.4%～0.5%时,循环初期表现出循环硬化的现象,而后循环软化。合金的疲劳裂纹萌生于试样表面,裂纹扩展区存在明显的疲劳条带,合金疲劳断口呈现韧性断裂特征。     

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.     

Enhanced fracture assessment under biaxial external loads using small scale cruciform bending specimens

The present study is concerned with an enhanced fracture mechanics characterization of engineering materials using small scale cruciform bending specimens. Based on the regular SE(B) specimen geometry with a shallow crack, two additional loading legs allow the application of an additional stress component acting longitudinally to the crack front. Compared to standard specimen types, the biaxial loading conditions for the cruciform specimens are in general closer to the situation in pressurized vessels and pipes, especially under thermal shock loading conditions. In a combined experimental and numerical approach, detailed assessments of the local stress and strain fields in comparison to the crack front stress and strain states of standard specimens with deep and shallow cracks are provided. The cruciform bending specimen geometry is demonstrated to be suitable even in small scale dimensions. It permits the application of different combined external loading situations and thus a fracture assessment under conditions close to various situations in engineering application. Due to its small size, the specimen geometry can be employed even if only a limited amount of material is available.     

Ein einfaches Verfahren zur Bestimmung gültiger Bruchzähigkeitswerte von Hartmetallen

A Simple Method of Determining Valid Fracture Toughness Data of Cemented Carbides From a comparison of published data it follows that a valid determination of the fracture toughness of cemented carbides depends on the use of samples containing sharp cracks. It is shown that using the technique of controlled fracture experiments sharp cracks of a given length can be introduced easily and reproducibly into bend specimens. A new evaluation method permits the fracture toughness to be calculated without knowing the crack length if the compliance of the pre-cracked specimen is measured. The K_Ic values determined in this way are characterized by a very small scatter and agree well with data from the literature which were obtained from specimens of similar composition. A comparison of the flaw size calculated from K_Ic and the bend strength to the failure size detected in fractographic studies shows very good agreement.     

Influence of microstructure on the cyclic crack growth in a low-alloy steel

Fatigue tests have been performed on compact type and 4-point bend specimens of a low-alloy steel BS4360-50D in air at 30 Hz and at various stress ratios to determine the influence of microstructure on the fatigue crack propagation. Region I of the crack growth showed crystallographic facets, while two classes of secondary cracks were observed in Region II. Ductile tearing occurred in Region III and some dimple formation was also observed.     

Constraint effects at brittle fracture initiation in a cast ferritic steel

The fracture resistance of a cast low carbon manganese ferritic steel intended for containers for spent nuclear fuel has been analysed by combining several approaches. Based on data from three-point bend specimens with shallow and deep cracks the effect of crack tip constraint at brittle fracture initiation has been followed. Q-parameter was used for the constraint quantification. The crack length effect on the fracture toughness–temperature diagram has been analysed and peculiarities of fracture behaviour in the lower shelf region have been explained. The role of cleavage fracture stress in brittle fracture initiation under the influence of crack tip constraint has been analysed.     

Effect of fracture path on the toughness of weld metal

The crack propagation direction may affect weld metal fracture behavior. This fracture behavior has been investigated using two sets of single edge notched bend (SENB) specimens; one with a crack propagating in the welding direction (B×2B) and the other with a crack propagating from the top in the root direction (B×B) of a welded joint. Two different weld metals were used, one with low and one with high toughness values. For Weld Metal A, two specimen types have been used (B×B and B×2B) both with deep cracks. The weld metal A (with high toughness values) has reasonably uniform properties between weld root and cap. The resulting J-R curves show little effect of the specimen type, are ductile to the extent that the toughness exceeds the maximum J_max, value allowed by validity limits and testing is in the large –scale yielding regime. In the case of weld metal B (with low toughness values) with two specimen types (B×B and B×2B) the B×B specimen has shallow cracks while the B×2B specimen has deep cracks. Both resulting J-R curves show unstable behavior despite the fact that the types of specimen and their constraints are different. The analysis has shown that crack propagation direction is most influential for a weldment with low toughness in the small scale yielding regime, whereas its influence diminishes due to ductile tearing during stable crack growth and large scale yielding. The results have shown that these effects are different in both the crack initiation phase and during stable crack growth, indicating a dependence on weld metal toughness and the microstructure of the weld metal. It can be concluded that, if resistance curves during stable crack growth do not show differences in both notch orientations, the fracture toughness values of the whole weld metal can be treated as uniform.     

FINITE ELEMENT AND EXPERIMENTAL STUDIES OF CRACK GROWTH IN CLADDED SEN(B) SPECIMENS

Abstract— The transferability of fracture results between homogeneous and cladded specimens was studied in single edge-notched bend specimens. The test material was of A533-B steel with a clad layer deposited by a commercial strip welding process. The fracture resistance properties were developed independently for cladding and base material using homogeneous specimens of each material. The experimental data from tests on cladded specimens were analysed with the finite element method. The 3D J -values were compared with values evaluated using the measured crack extension in the cladded specimen and the J _R-data of the respective material provided from homogeneous specimens. A reasonably good agreement was obtained in this comparison for a limited amount of crack growth.     

Effect of side-grooving on the compliance of the cantilever bend specimen

The precracked cantilever bend specimen, which is normally employed to determine the stress corrosion cracking threshold $\text{K}{}_{\mathrm{Iscc}}$, can also be used to obtain the stress corrosion crack growth rate as a function of stress intensity factor $\text{K}{}_{\mathrm{I}}$. When the crack is obscured, crack growth can be monitored by measuring the crack-opening displacement and converting this to crack length by means of the compliance relationship for the specimen. Compliance relationships were therefore determined for 0.5-in.-thick AISI 4340 steel cantilever bend specimens with net-to-gross thickness ratios of 1.0 (no side grooves), 0.8(shallow side grooves), and 0.6 (deep side grooves). The shallow side grooves had no effect on the crack-opening compliance relationship, while the deep side grooves increased the crack-opening compliance by about 20%.