Effect of size on plasticity and fracture toughness

The effect of thickness and width of CT specimens on the plastic zone size has been investigated. The investigation also examines the applicability of the various approaches to fracture toughness measurements such as ASTM E399 K_Ic, J_Ic, R-curve and a new procedure of K_Ic determination proposed recently, to a steel which has medium strength and which undergoes pop-in type unstable crack extension during the toughness testing. The results show that in CT specimens with a constant aspect ratio prepared from a given material and loaded to a given stress intensity factor, the plastic zone size decreases, as the specimen width increases; on the other hand, the thickness has only a comparatively small effect on the plastic zone size. The new procedure of K_Ic determination is verified with experiments on specimens with width to thickness ratio of about 50 and it gives a size independent K_Ic value in specimens whose thickness is 4.5 times less than that required by ASTM E399. The new procedure gives a meaningful value of K_Ic in a situation where all other methods such as ASTM E399 K_Ic, J_Ic and R-curve approach are observed to be inapplicable.     

断裂韧性测试中的载荷分离法及应用

针对无法直接获得载荷(P)-加载线位移(load line displacement,LLD)对应的塑性功导致无法直接完成基于直通型紧凑拉伸试样(front face compact tension,FFCT)试样材料断裂韧性测试的问题,该文基于迭代理念将适用于台阶型试样(load line compact tension,LLCT)的规则化法推广应用于FFCT试样,得到基于FFCT试样评估延性材料断裂韧性的可行方法.结合汽轮机转子钢和迭代方法,验证新方法准确性,最后将迭代方法应用于核反应堆材料A508-Ⅲ钢的J阻力曲线测试中,有助于解决基于1/2FFCT试样获取断裂韧性的难题.     

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.     

Alternative test method for interlaminar fracture toughness of composites

Two methods of determining the mode I interlaminar fracture toughness for fiber-reinforced polymer matrix (FRPM) composites using a double cantilever beam (DCB) test are compared. The standard method of determining G _IC is based in linear-elastic fracture mechanics theory and requires a visual measurement of the crack length, presenting data acquisition and analysis difficulties. The proposed method makes use of elastic–plastic fracture mechanics theory and an analytical closed form solution to the J-integral to relate the fracture toughness J _IC , load, and angular displacement at the load application points. This method has the advantage of replacing visually acquired data with data easily obtained using inexpensive transducers as well as being applicable to a broader class of materials.     

Fatigue fracture toughness and crack propagation rate

Fatigue crack growth rate, da/dN, of two high strength steels were examined in a laboratory air at different stress ratios, covering almost the entire range of stress intensity, K, from nearly threshold value, Kth, to final fracture. The fatigue fracture toughness, Kfc, corresponding to the final fracture in fatigue, was also determined. The lower the Kfc, the higher da/dN and reduced Kth are revealed.This correlation was analyzed quantitatively based on the four parameter Weibull function. And the stress ratio dependency of the fatigue crack propagation curve can be cleared in a successful manner.The fatigue characteristic stress intensities, Ke and Kv, are proposed to define the transition behaviour in fatigue crack growth curve, from so called region 1 to 2, and from region 2 to 3, respectively. Especially the Kv valua can be specified to be the 0.63Kfc.

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Résumé On a étudié la vitesse de propagation de fissure en fatigue da/dN de deux aciers à haute résistance dans un atmosphère de laboratoire sous des sollicitations couvrant toute la gamme des intensités de contraintes variables K, depuis une valeur voisine de la valeur du seuil Kth jusqu'à celle correspondant à rupture finale.La ténacité à la rupture par fatigue Kfe correspondant à la rupture finale par fatigue a été également déterminée. II s'avère que plus Kfe est faible, plus élevée est da/dN et plus Kth est réduite. Cette correlation est analysée quantitativement en se basant sur la fonction de Weibull à quatre paramètres. On peut ainsi clarifier la manière dont le rapport de contraintes influe les courbes de propagation des fissures de fatigue.On propose de définir pas les facteurs caractéristiques d'intensité de contrainte Ke et Kv les comportements de transition de la courbe de vitesse de propagation de la fissure entre respectivement les régions dénommées 1 et 2, et 2 et 3.En particulier, on peut spécifier que la valeur Kv vaut 0,63 Kfe.

     

Stress intensity calibrations and compliance functions for fracture toughness and crack propagation test specimens

Experimental determination of compliance over the approximate range of a/W from 0.3 to 0.7 has been undertaken for compact tension and cantilever beam test specimens. The test data have been processed using a recently proposed analytical procedure, and the results for compliance functions have been compared with some standard results available in the literature. The agreement between the experimental results and the proposed compliance functions equation for compact tension geometry of ASTM E399 is excellent. However, for the cantilever beam specimen, it is demonstrated that the usual Srawley and Brown equation for pure bending may underestimate the compliance function by as much as 14%.     

Influence of dynamic fracture toughness on dynamic crack propagation

A dynamic finite element code was used in its “propagation mode” to assess the differences in dynamic crack propagation in a wedge-loaded (WL) single-edged notch (SEN) specimen, a tapered double cantilever beam (TDCB) specimen and a rectangular double cantilever beam (RDCB) specimen. The dynamic fracture toughness, K_ID, vs the crack velocity, a, relations determined experimentally for WL-SEN, WL-TDCB and WL-RDCB specimens machined from Araldite B were used as dynamic fracture criteria and the resultant k_id variations with crack propagations in the three specimens were compared with the corresponding experimental results. While the specific K_ID vs /.a relations established for each specimen obviously yielded calculated k_ID which were in best agreement with the experimental K_ID for the respective specimen, the K_ID vs /.a relation for the large WL-SEN specimen provided the best overall fit between the calculated and measured K_ID variations with crack propagation in all three specimens.     

The temperature wave method of determining fracture toughness values due to crack propagation

A method is presented of determining fracture toughness by measurement of the amount of heat emitted at the tip of a propagating crack. Two thermojunctions placed adjacent to the crack were used to monitor the temperature wave produced at fracture. An electromagnetic fluxmeter was used to integrate the thermojunction output with respect to time and was calibrated to give a direct reading in terms of strain energy release rate G. The temperature wave method is independent of initial crack length and fracture surface area and can be readily used for specimens having complex sections. Values obtained by this method compare favourably with toughness values determined by a linear elastic fracture mechanics analysis. Results of static and dynamic three-point bending tests on specimens at different temperatures within the range ?40 to 60° C are reported.     

The effects of constraint on crack tip fields and fracture toughness

The detailed stresses, deformations and porosities in the vicinity of a blunting crack in different fracture specimens, Single Edge Notch (SEN), Three Point Bending (TPB) specimens, and Small Scale Yielding (SSY) model were studied by the larger deformation finite element method. The presence and subsequent growth of smaller scale voids were taken into account by using a modified Gurson's model to describe the constitutive behavior of the material. The dependences of the stresses, deformations and porosities on specimen configurations were associated with the crack tip constraint. The porosity in the tip region, along with the void coalescence criterion, were used to predict the macroscopic fracture toughness as a function of the constraint, and a comparison with experimental data was performed in this paper.     

Influence of specimen size and configuration on the plastic zone size, toughness and crack growth

The main purpose of this investigation is to evaluate the effect of the thickness, width, aspect ratio and geometry of the fracture toughness specimen on the resultant displacement due to growth of plastic zone and crack.

The analytical part evaluates the effect of the width, aspect ratio, geometry and flow properties on the displacement due to the growth of plastic zone as well as the crack. The experimental part evaluates the effect of thickness and width of a compact tension specimen on the displacement and on the thickness direction contraction due to the growth of the plastic zone.

The main result of the investigation is that the plastic zone size decreases and the constraint to yielding increases as the width of a CT specimen increases. Based on this and other analytical and experimental result, a new procedure for the determination of K_IC has been proposed. The procedure is verified by experimental data obtained by other workers. The procedure overcomes the limitation of ASTM E399 for the determination of K_IC.     

Relationship between fracture toughness and deformation ahead of the crack tip

An analytical relationship for the calculation of the intensity of elastoplastic strains at the front of a mode I crack is obtained on the basis of the suggested model. A strain criterion of fracture toughness has been developed which relates the stress intensity factor to the width of the stretch zone, the mechanical properties of the material, and its elastic constants. A comparison of experimental and numerical (obtained by using the proposed equations) data of the stretch zone width for 15Kh2NMFA steel in a wide temperature range demonstrates good agreement between the theory and the experiment. This proves the possibility of calculating fracture toughness via the stretch zone width and mechanical properties of the material. Translated from Problemy Prochnosti, No. 2, pp. 33–40, March–April, 1997.     

Role of crack size in the bi-modal static fatigue failure of a cordierite glass and glass-ceramic

A study was conducted of the static fatigue behaviour at room temperature of a cordierite glass and glass-ceramic with model flaws of two different sizes introduced by the indentation fracture method. For the cordierite glass the stress intensity exponent, N, for sub-critical crack growth inferred from the dependence. of time-to-failure on stress was the same for the two different crack sizes and showed good agreement with the value of N for data obtained in an earlier study for dynamic fatigue and by the double-torsion method. For the cordierite glass-ceramic, which consisted of larger crystallites (a few micrometres in size) embedded in a primarily crystalline fine-grained matrix, the static fatigue response depended strongly on crack size, also observed during dynamic fatigue. This effect was attributed to the relative size difference between the cracks and the crystallites. The small cracks could propagate in a planar fashion, whereas the larger cracks were subject to toughening by crack-deflection around the crystallites and a corresponding decrease in the rate of sub-critical crack growth. An analysis for the case of idealized bi-modal crack-size dependent sub-critical crack-growth indicated that, for a cordierite glass-ceramic with small cracks, the role of the larger crystallites serves to introduce a pseudo fatigue-limit.On sabbatical leave from Department of Ceramic Engineering, Yonsei University, Seoul, Korea.