Measurement of fracture initiation toughness and crack resistance in instrumented Charpy impact testing

A new method has been developed involving direct measurement of the load-line displacement during instrumented Charpy testing. The method uses a laser interferometer to measure displacement in addition to the load-line displacement derived from the load signal. Tests were conducted using fatigue precracked and V-notched test pieces in the temperature range +23°C to −80°C on a conventional ship grade steel, a pressure vessel steel and two welded joints. Good correlation was found between the J_0.2 initiation fracture toughness determined by the multi-specimen method and the J_i fracture toughness determined from single specimens using the new method to detect ductile fracture initiation.     

Toughness and microscopic fracture mechanisms of unfilled and short-glass-fibre-filled poly(cyano arylether)

Fracture mechanisms of an advanced high-strength thermoplastic poly(cyano arylether) (PCAE) and its short-glass-fibre (SGF)-reinforced composites have been studied in relation to toughnesses K _c and J _c. Test temperatures were 23 and 100 °C. Reflected and transmitted optical observations were combined with scanning electron microscopy for the fractographic investigation. For unreinforced PCAE tested at 100 °C, the damage area in front of a notch becomes fairly large in size and consists of numerous tensile microfailures around the local plastic yielding zone, as compared with that tested at 23 °C. This resulted in a substantial improvement of K _c and a big increase in J _c. Filling fibres, however, produced both toughening and anti-toughening results: effects of fibre spanning, pull-out and bridging across the local plastic failure zone and zigzag propagation of fracture due to fibre filling, improved the toughness. However, adhesive failure at the fibre-matrix interface, tensile microcleavage at the fibre ends and straightforward fracture in the skin layer, considerably diminished the values of K _c and J _c, except for the trend of K _c at 23 °C.     

Evaluation of the fracture toughness properties of polytetrafluoroethylene

Polytetrafluoroethylene (PTFE) (Dupont Tradename Teflon) is a common polymer with many structural applications including sheet, gaskets, bearing pads, piston rings and diaphragms. The interest here developed because this polymer is being considered as the major component of a newly proposed `reactive' material with a possible application as a projectile to replace common inertial projectiles. Little mechanical property data is available on this material since it is commonly used only as a coating material with the dominant properties being its low friction coefficient and high application temperature. Previous work (Joyce, 2003) on commercially available sheet PTFE material has demonstrated the applicability of the normalization method of ASTM E1820 (1999), the elastic-plastic fracture toughness standard to develop fracture toughness properties of this material over a range of test temperatures and loading rates. Additional work on the aluminum filled `reactive' derivative of the basic PTFE polymer (Joyce and Joyce, 2004) has also recently been completed. In this work, standard ASTM E1820 fracture toughness specimens machined from sintered pucks of PTFE were tested at four test temperatures and at a range of test rates to determine the J _Ic and J resistance curve characteristics of the PTFE material. The major results are that while crack extension is difficult at standard laboratory loading rates at ambient (21 °C) temperature or above, for temperatures slightly below ambient or for elevated loading rates, a rapid degradation of fracture resistance occurs and cracking occurs in a ductile or even nearly brittle manner.     

Specimen Size Requirements for Two-parameter Fracture Toughness Testing

Using a single parameter fracture mechanics theory, a minimum specimen size requirement of min(a, b, B) >200J/σ₀ in tension and min(a, b, B) >25J/σ₀ in bending, where B is the thickness, b the remaining ligament and a is the crack length of the specimen, were derived [Shih and German (1981), International Journal of fracture 17, 27–43] which have provided the basis for modern fracture toughness testing procedures. Two-parameter fracture toughness testing including the constraint, on the other hand, is desirable since it offers a solution to the transferability issue. A size requirement for a valid two-parameter fracture toughness testing based on the J-A₂ three-term solution was determined as min(a, b, B) > 11J/σ₀ [Chao and Zhu (1998), International Journal of fracture 89, 285–307] in which the limiting case is bend specimens under large scale yielding (LSY). Recent work by Chao et al. (2004, International Journal of fracture, 27, 283–302) has shown that the J-A₂ dominance at a crack tip can be significantly enhanced for bending specimens under LSY if a modified J-A₂ solution is adopted. This current paper further studies the size of the J-A₂ dominant zone using the modified J-A₂ solution for deep bend specimens with hardening from low to high and loading from SSY to LSY using finite element analysis. Based on the results, a rather relaxed specimen size requirement min(a, b, B) >6J/σ₀ is developed and recommended for a valid two-parameter fracture toughness testing using the J-A₂ fracture criterion. Validity of the size requirement is demonstrated by using the experimental J-R curves from non-standard bending specimens for A285 steel.     

Finite element simulation of fracture behaviour for aged duplex stainless steels

In this paper, the local approach model developed by Gurson–Tvergaard has been applied to simulate both the crack initiation and the crack growth of aged duplex stainless steel. The parameters of the Gurson–Tvergaard model have been obtained, from axisymmetric notched specimen testing, as a function of the ageing time at 400°C, the ferrite content of the steel and the stress triaxiality. After that, to simulate the fracture of CT specimens, finite element (FE) calculations have been effected in order to obtain the stress triaxiality value at each point on the process zone ahead of the crack tip of these specimens. The adequate damage parameters concerning triaxiality are determined from the ones obtained at the notched specimens, in order to be used in FE simulations of fracture behaviour. With them, the corresponding J−Δa curves have been simulated as representative of both the crack initiation and crack propagation stages, and compared with experimental results in order to validate the methodology proposed.     

Time-dependent deformation and fracture of steel between 20°C and 400°C

The time-dependent deformation and cracking behavior of the quenched and tempered steel 15 NiCuMoNb 5 was investigated in the temperature range 20°C to 400°C. Fracture mechanics tests were carried out under various loading conditions including load-hold times of up to three weeks. The time-dependent crack growth can be described by the crack resistance (J _R-) curve. Only above 300°C, the J _R-curves obtained from constant-load tests start to deviate substantially from constant-displacement-rate tests. In this temperature range, the C _t-parameter, which has been developed for creep crack growth testing, can be used to describe crack growth rates. For practical purposes, it is important to note that hold-time effects reduce the load-bearing capacity of cracked specimens by less than 10 percent for the present material and testing conditions.

---

Résumé On a étudié la déformation en fonction du temps et le comportement à la fissuration entre 20 et 400°C de l'acier trempé et revenu 15 NiCuMoNb 5. On a procédé à des essais de mécanique de rupture sous diverses conditions de mise en charge, y compris un maintien de la charge sur des durées allant jusqu'à trois semaines. On peut décrire la croissance en fonction du temps de la fissure par la courbe de résistance à la fissuration J _R. Ce n'est qu'au delà de 300°C que les courbes J _R obtenues par des essais à charge constante commencent à dévier de manière substantielle de celles obtenues par des essais à vitesse de déplacement constante. Dans cette gamme de température, le paramètre Ct qui a été conçu pour les essais de croissance de fissures de fluage, peut être utilisé pour décrire la vitesse de croissance de la fissure. Pratiquement, il est intéressant de noter que les effets de maintien de la charge sont de réduire la capacité de portance des échantillons fissurés de moins de 10%, et ceci pour les conditions de matériaux et d'essais adoptées.

     

Relation of Slow Crack Growth Failure Time to Structure of HDPE

Long-time brittle failure limits the lifetime of polyethylenepipes for water and gas distribution. The same type of failure wasobserved in single-edge-notched tensile specimens under plane strainconditions. The crack opening displacement (COD) was measured as afunction of time and temperature, and the time to complete fracture(t _f ) was measured. An empirical failure time extrapolationrelation based on temperature was developed using the Arrheniusequation. The experimental and extrapolated data for80°C were found to correlate very well. Using thisrelation, structural parameters were characterised by the StepwiseIsothermal Segregation/Differential Scanning Calorimetry (SIS/DSC)method. The correlation between fracture and structural parameters wasfound.     

Constraint-modified J−R curves and its application to ductile crack growth

The concept of J-controlled crack growth is extended to J–A ₂ controlled crack growth using J as the loading level and A ₂ as the constraint parameter. It is shown that during crack extension, the parameter A ₂ is an appropriate constraint parameter due to its independence of applied loads under fully plastic conditions or large-scale yielding. A wide range of constraint level is considered using five different types of specimen geometry and loading configuration; namely, compact tension (CT), three-point bend (TPB), single edge-notched tension (SENT), double edge-notched tension (DENT) and centre-cracked panel (CCP). The upper shelf initiation toughness J _IC, tearing resistance T _R and J–R curves tested by Joyce and Link (1995) for A533B steels using the first four specimens are analysed. Through finite element analysis at the applied load of J _IC, the values of A ₂ for all specimens are determined. The framework and construction of constraint-modified J–R curves using A ₂ as the constraint parameter are developed and demonstrated. A procedure of transferring the J–R curves determined from standard ASTM procedure to non-standard specimens or practical cracked structures is outlined. Based on the test data, the constraint-modified J–R curves are presented for the test material of A533B steel. Comparison shows the experimental J–R curves can be reproduced or predicted accurately by the constraint-modified J–R curves for all specimens tested. Finally, the variation of J–R curves with the size of test specimens is produced. The results show that larger specimens tend to have lower crack growth resistance curves.     

Mixed-mode fracture load prediction in lead-free solder joints

Double cantilever beam (DCB) fracture specimens were made by joining copper bars with both continuous and discrete SAC305 solder layers of different lengths under standard surface mount (SMT) processing conditions. The specimens were then fractured under mode-I and various mixed-mode loading conditions. The loads corresponding to crack initiation in the continuous joints were used to calculate the critical strain energy release rate, J_ci, at the various mode ratios using elastic–plastic finite element analysis (FEA). It was found that the J_ci from the continuous joint DCBs provided a lower bound strength prediction for discrete 2 mm and 5 mm long joints at the various mode ratios. Additionally, these J_ci values calculated from FEA using the measured fracture loads agreed reasonably with J_ci estimated from measured crack opening displacements at crack initiation in both the continuous and discrete joints. Therefore, the critical strain energy release rate as a function of the mode ratio of loading is a promising fracture criterion that can be used to predict the strength of solder joints of arbitrary geometry subject to combined tensile and shear loads.     

DAMAGE MECHANICS APPROACH TO REMOVE THE CONSTRAINT DEPENDENCE OF ELASTIC–PLASTIC FRACTURE TOUGHNESS

It is now generally agreed that the applicability of a one-parameter J-based ductile fracture approach is limited to so-called high constraint crack geometries, and that the elastic-plastic fracture toughness J_1c, is not a material constant but strongly specimen geometry constraint-dependent. In this paper, the constraint effect on elastic-plastic fracture toughness is investigated by use of a continuum damage mechanics approach. Based on a new local damage theory for ductile fracture(proposed by the author) which has a clear physical meaning and can describe both deformation and constraint effects on ductile fracture, a relationship is described between the conventional elastic-plastic fracture toughness, J_1c, and crack tip constraint, characterized by crack tip stress triaxiality T. Then, a new parameter J_dc (and associated criterion, J_d=J_dc) for ductile fracture is proposed. Experiments show that toughness variation with specimen geometry constraint changes can effectively be removed by use of the constraint correction procedure proposed in this paper, and that the new parameter J_dc is a material constant independent of specimen geometry (constraint). This parameter can serve as a new parameter to differentiate the elastic-plastic fracture toughness of engineering materials, which provides a new approach for fracture assessments of structures. It is not necessary to determine which laboratory specimen matches the structural constraint; rather, any specimen geometry can be tested to measure the size-independent fracture toughness J_dc. The potential advantage is clear and the results are very encouraging.     

Mixed-mode high temperature toughness of silicon nitride

Both opening-mode and mixed-mode fracture toughness tests were carried out at 1200 and 1300 °C on a sinter/HIP grade of silicon nitride. Data for pure opening loading (K _Ic) agree well with other experiments on the same material, which showed that the toughness was lower at 1000 °C than at room temperature, but increased as temperature increased above 1000 °C. The ratio of K _IIc/K _Ic was sufficiently insensitive to temperature that it can be considered to be constant. Results are discussed in the context of mechanisms that have been proposed to explain fracture toughness in silicon nitride.     

Adherence properties of metal-to-ceramic joints

A study is reported of the fracture mechanics of metal-to-ceramic laminates (Al₂O₃/Nb, Si₃N₄/Zr) produced by solid-state bonding. The bond quality of notched bend and tension specimens is described in terms of a stress intensity factor K _ICV, which is evaluated in the same way as for isotropic material. K _ICV is measured as functions of the microstructure of the constituents, the metal layer thickness, the environmental conditions and the test temperature. At very high test temperatures where plastic flow occurs, the J-integral was used for bond quality characterization. For the linear elastic case, the J-value is compared with the stress intensity concept K _ICV. In contrast to the behaviour of a bulk ceramic material, the J-value increases with increasing test temperature if a thick metal layer (3 mm) is used.     

Application of the method of caustics to the centre-cracked diametral compression test specimen

Normalized Mode I stress intensity factors,N ₁(a/R), for symmetrical radial cracks in diametral compression test specimens were experimentally evaluated using disc specimens of polymethyl methacrylate and the method of caustics. The method of caustics was first employed with precracked three-point bend specimens to assess the optical constant for the test material. This material property and the diameters of the caustics as a function of the applied load at different relative crack lengths (a/R) yielded the non-dimensional stress intensity factors using equations presented by Theocaris. These experimental values agreed closely with the theoretical solutions reported in the literature. Disc specimens of a polycrystalline alumina were also tested in diametral compression at temperatures up to 1000° C and the measured fracture toughness values were compared to those measured with chevron-notched bend specimens. It is shown that the centre-cracked diametral compression specimens give very reproducible fracture toughness measurements, and the specimen and the test technique can be usefully employed to assess the fracture toughness of structural ceramics at both ambient and elevated temperatures.     

J-integral studies of crack initiation of a tough high density polyethylene

The J-integral is applied to characterise the fracture initiation of a tough high density polyethylene for which the concepts of linear elastic fracture mechanics (LEFM) are inapplicable for reasonably sized specimens due to extensive plasticity. The multiple specimen resistance curve technique recommended by the ASTM is the basic method employed. A formulation based on the finite difference in crack area between two otherwise identical specimens is used to determine J _Ic for comparison with the result obtained from the basic method. A comparison is also made with the results obtained from the Bilby, Cottrell & Swinden (BCS) model of yielding ahead of a crack.Tests are performed in the temperature range from +23°C to –80°C.

---

Résumé On applique l'intégrale J à la caractérisation de l'amorçage d'une rupture dans un polyéthilène tenace à haute densité pour lequel les concepts de la théorie linéaire élastique de la mécanique de rupture sont inapplicables dans le cas d'éprouvette de dimension raisonnable, en raison d'une plasticité étendue. La méthode de base utilisée est la technique de la courbe de résistance d'une éprouvette multiple, telle que recommandée par l'ASTM. Une formulation basée sur les différences finies dans la zone de fissuration entre deux éprouvettes identiques par ailleurs, est utilisée à la détermination de J_Ic en vue d'une comparaison avec les résultats obtenus à partir de la méthode de base. Une comparaison est également effectuée avec les résultats obtenus par l'utilisation du modèle de Bilby, Cottrell et Swinden relatif à l'écoulement plastique en avant de la fissure.Les essais ont été effectués dans une gamme de températures comprise entre +23°C et –80°C.

     

Further developments in <Emphasis Type="Italic">J</Emphasis> evaluation procedure for growing cracks based on LLD and CMOD data

Laboratory testing of fracture specimens to measure resistance curves (J − Δa) have focused primarily on the unloading compliance method using a single specimen. Current estimation procedures (which form the basis of ASTM E1820 standard) employ load line displacement (LLD) records to measure fracture toughness resistance data incorporating a crack growth correction for J. An alternative method which potentially simplifies the test procedure involves the use of crack mouth opening displacement (CMOD) to determine both crack growth and J. However, while the J-correction for crack growth effects adopted by ASTM standard holds true for resistance curves measured using load line displacement (LLD) data, it becomes unsuitable for J-resistance measurements based upon the specimen response defined in terms of load-crack mouth opening displacement (CMOD). Consequently, direct application of the evaluation procedure for J derived from LLD records in laboratory measurements of resistance curves using CMOD data becomes questionable. This study provides further developments of the evaluation procedure for J in cracked bodies that experience ductile crack growth based upon the eta-method and CMOD data. The introduction of a constant relationship between the plastic components of LLD (Δ _p ) and CMOD (V _p ) drives the development of a convenient crack growth correction for J with increased loading when using laboratory measurements of P-CMOD data. The methodology broadens the applicability of current standards adopting the unloading compliance technique in laboratory measurements of fracture toughness resistance data (J resistance curves). The developed J evaluation formulation for growing cracks based on CMOD data provides a viable and simpler test technique to measure crack growth resistance data for ductile materials.     

Temperature and deformation rate dependence of the work of fracture in polycarbonate (PC) film

Single edge notched polycarbonate (PC) specimens of thickness 0.175 mm were pulled to complete fracture at temperatures between 25°C and 100°C and at loading rate values of 2, 5 and 50 mm/min. A duckbill-shaped yielded zone was formed ahead of the crack tip in all the specimen tested. Propagation of the crack within the yielded zone was always stable. The method of essential work of fracture (EWF) was used to study the effects of temperature and loading rate on fracture toughness. The specific essential work of fracture, w _e, was found to be independent of both temperature and loading rate. The non-essential work of fracture, w _p, increased with increasing temperature but showed no systematic variation with respect to loading rate. Moreover, plastic constraint factor, m, also increased with increasing temperature. A linear temperature dependence was obtained for both w _p and m giving the extrapolated values of w _p = 0 and m = 0.5 at –23°C.     

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.     

Effects of weld strength mismatch on <Emphasis Type="Italic">J</Emphasis> and CTOD estimation procedure for SE(B) specimens

This work examines the effect of weld strength mismatch on fracture toughness measurements defined by J and CTOD fracture parameters using single edge notch bend (SE(B)) specimens. A central objective of the present study is to enlarge on previous developments of J and CTOD estimation procedures for welded bend specimens based upon plastic eta factors (η) and plastic rotational factors (r _p ). Very detailed non-linear finite element analyses for plane-strain models of standard SE(B) fracture specimens with a notch located at the center of square groove welds and in the heat affected zone provide the evolution of load with increased crack mouth opening displacement required for the estimation procedure. One key result emerging from the analyses is that levels of weld strength mismatch within the range ±20% mismatch do not affect significantly J and CTOD estimation expressions applicable to homogeneous materials, particularly for deeply cracked fracture specimens with relatively large weld grooves. The present study provides additional understanding on the effect of weld strength mismatch on J and CTOD toughness measurements while, at the same time, adding a fairly extensive body of results to determine parameters J and CTOD for different materials using bend specimens with varying geometries and mismatch levels.     

Fracture behavior of stitched warp-knit fabric composites

Pilot studies are conducted to characterize the macroscopic fracture resistance behavior using linear elastic fracture mechanics and attempt to quantify the fracture parameters in which may govern the fracture and failure patterns of stitched warp-knit fabric composites. Methods based on the J-integral method and Betti's reciprocal theorem in extracting the fracture parameters, critical stress intensity factors, T-stress, and the second term of _y(r,0) near the crack tip prior to fracture initiation are formulated. Two fracture criteria, [_c,r _c] and [_c,r _c] are attempted to characterize the failure initiation for the fiber-dominated failure mode and self-similar crack extension in a given thickness of the laminate. Based on linear elastic fracture mechanics principle, these criteria are transformed into crack-driving forces [K _Q,T] and [K _Q,g ₃₂]. The two-parameter fracture criteria, [K _Q,T] and [K _Q,g ₃₂] provide a good correlation for the CCT and SENT specimens, but not for the high constraint CT specimens. With the limited experimental data, the results tend to show that the large tensile T-stress and large magnitude of negative g ₃₂ may inhibit the crack extension in the same crack plane and promote crack kinking.     

Residual strength of unidirectional fibre-metal laminates based on JC toughness of C(T) and SE(B) specimens: comparison with M(T) test results

Fibre‐metal laminates (FMLs) are structural composites designed with the aim of producing very low fatigue crack‐propagation rate, damage‐tolerant and high‐strength materials, if compared to aeronautical Al alloys. Their application in aeronautical structures demands a deep knowledge of a wide set of mechanical properties and technological values, including both fracture toughness and residual strength. The residual strength of FMLs have been traditionally determined by using wide centre‐cracked tension panels M(T). The use of this geometry requires large quantities of material and heavy laboratory facilities. In this work, fracture toughness ( J_C) of some unidirectional FMLs laminates was measured using a recently proposed methodology for critical fracture toughness evaluation on compact tension C(T) and single‐edge bend SE(B) specimens. Additionally, residual strength values of wider M(T) specimens with different widths (W from 150 to 200 mm) and several crack to width ratios (2a/W) were experimentally obtained. Some experimental residual strength values of M(T) specimens (W from 150 to 400 mm and different 2a/W ratios) of Arall were also obtained from the bibliography. Based on J_C results from C(T) and SE(B) specimens, and either using or not using crack‐tip plasticity corrections, the residual strengths of the M(T) specimens were predicted and compared to the experimental ones. The results showed good agreement, especially when crack‐tip plasticity corrections were applied.