Crack velocity dependence of longitudinal fracture in bone

An evaluation of the fracture characteristics of bovine tibia compact tension specimens associated with controlled crack propagation in the longitudinal direction has been made. The fracture mechanics parameters of critical strain energy release rate (G _c) and critical stress intensity factor (K _c) were determined for a range of crack velocities. A comparative fracture energy (W) was also evaluated from the area under the load-deflection curve. It was found that an increase in the average crack velocity from 1.75 to 23.6×10^–5 m sec^–1 produced increases in G _c (from 1736 to 2796 J m^–2), K _c (from 4.46 to 5.38 MN m^–3/2) and W. At crack velocities >23.6×10^–5 m sec^–1, W decreased appreciably. Microstructural observations indicated that, for crack velocities <23.6 m sec^–1, relatively rough fracture surfaces were produced by the passage of the crack around intersecting osteons (or lamellae), together with some osteon pull-out. In contrast, at a higher crack velocity, fracture was characterized by relatively smooth surfaces, as the crack moved indiscriminately through the microstructural constituents.     

Comparison of methods for fracture toughness testing of thin low carbon steel plates

Abstract

The fracture toughness of double edge notched tension (DENT) specimens of a low carbon steel sheet was evaluated using experimental and numerical methods. The concepts of critical J integral J_c critical crack tip opening displacement δ_c, essential work of fracture We_e, and essential work of fracture and initiation we^init were compared. The numerical methods were based on finite strain, three-dimensional finite element simulations of the tensile straining of the DENT specimens. Good agreement was found between numerical and experimental J_c values. Fair agreement was also found between J_c and we^init. The essential work of fracture W_e was ～20% lower than J_c. This discrepancy is attributed to inaccuracy in the detection of cracking initiation. The Shih factor derived from the measured J_c and δ_c values closely corresponds with the plane stress prediction.     

Relation between work of fracture and fracture toughness of short-fibre reinforced polymers

On the basis of micromechanical failure mechanisms acting in short-fibre reinforced polymers we derive the crack resistance curve (R-rmcurve) as a function of crack extension. With the conditions characterizing the point of crack instability, the critical crack extension and fracture toughness, G_c, are calculated. By comparing G_c to the work of fracture we are able to conclude that, depending on the relevant failure characteristics, two parameters are necessary to describe the failure behaviour—the fracture toughness for crack instability or strength and the work of fracture as the energy necessary to drive the crack through the sample.     

On the application of the damage work density as a new initiation criterion for ductile fracture

In this paper the ‘damage work’ proposed by Chaouadi et al. is used to formulate an energy crack initiation criterion to describe ductile crack initiation. The traditional assessment of structural integrity by the J-integral, a property of elastic-plastic fracture mechanics is compared. Two free-cutting and one structural steel are investigated. The measured values for the critical damage work density at initiation W_di are compared with values for copper and RPV steel. As the fracture mechanical approach is limited to sharp cracks in the material (high-constraint stress state) the present damage mechanics approach is regarded as important as a more general concept closer to reality. While old void growth models of damage mechanics cannot formulate a simple criterion for crack initiation the applied damage work reaches a constant value at initiation W_di which is independent of the stress state during the deformation process. We recommend W_di as a material property of toughness for testing and engineering purposes.     

A failure criterion for brittle and quasi-brittle materials under any level of stress concentration

In this paper, we present a new criterion to predict the crack initiation under quasi-static loads from a geometrical weakness presenting an arbitrary stress concentration in brittle or quasi-brittle materials. Three material parameters were used in the establishment of the criterion, namely the ultimate stress σ_c, the critical energy release rate for crack growth G_c and the critical energy release rate for fracture under uniform uniaxial tension G_u. The use of these two critical energy release rates was justified by the observation of the fracture surfaces under different stress concentrations. The proposed three parameters’ concept enables to take the different stress concentration levels into account, thus provides a unified criterion to predict crack initiation for any stress concentration, whatever it is singular or regular. Numerous experimental studies were selected to verify the accuracy and efficiency of the criterion. It was shown that the proposed criterion is physically reasonable, highly accurate and easy to apply. It can be used in crack initiation prediction of engineering structures made of brittle or quasi-brittle materials.     

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.     

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.     

Experimental analysis of the practical LBZ effects on the brittle fracture performance of cryogenic steel HAZs with respect to crack arrest toughness near fusion line

Focusing on crack arrest behavior, this study investigates the practical influence of local brittle zones (LBZs) on the brittle fracture resistance of heat-affected zones (HAZs) in advanced 9% Ni cryogenic steel welds, and discusses whether the LBZs of this steel in practice have potentially deleterious effects as previously thought, or not. By analyzing the variations in brittle crack arrest toughness (K_a) and brittle crack initiation toughness (K_c) within actual HAZ, it is found that LBZs of this steel may not be harmful in consideration of crack arrest toughness near fusion line.     

Fracture toughness measurement by cylindrical specimen with ring-shaped crack

A method for measuring the plane strain fracture toughness of metals by means of cylindrical specimen in tension with axi-symmetrical ring-shaped crack is discussed. Owing to the fact that the crack tip of such a specimen is closer to ideal plane strain state, the K_1c value measured is effective and reliable. This investigation has fairly satisfactorily solved the problems of crack prefabrication, experimental technique, data processing and requirements for specimen dimensions.In both safety evaluation and life estimation of engineering components by linear elastic fracture mechanics, it is necessary to measure the fracture resisting parameter—fracture toughness under plane strain. According to the ASTM-E399-74 standard[1], when measuring the fracture toughness K_1c values of medium and low strength steels with a standard compact tension specimen or three-point bending specimen, it is necessary to use specimens of large dimensions, great tonnage fatigue testing machine and universal testing mechine. Naturally, this presents great difficulties to the investigation and application of fracture mechanics and it is precisely for the purpose of overcoming these difficulties that we have studied the method of measuring the plane strain fracture toughness by a cylindrical specimen in tension with axi-symmetrical ring-shaped crack. This method has fairly satisfactorily solved the problems of crack prefabrication, experimental technique, data processing and requirements for specimen size. Owing to the fact that the field around the crack tip of such a specimen is closer to ideal plane strain state, the results obtained are values smaller than those by using compact tension and three-point bending specimens and are more reliable fracture resisting constants for materials in linear elastic fracture mechanics analysis. Moreover, this method is more practical and economical because no expensive large fatigue testing machine is needed and the specimen size is small.     

Microstructural aspects of the fracture process in human cortical bone

Fracture toughness tests were conducted in the transverse and longitudinal directions to the osteonal orientation of human femoral cortical bone tissue to investigate the resulting damage patterns and their interaction with the microstructure. The time history of damage accumulation was monitored with acoustic emission (AE) during testing and was spatially observed histologically following testing. The fracture toughness of the transverse specimens was almost two times greater than the fracture toughness of the longitudinal specimens (3.47 MNm^–3/2 vs. 1.71 MNm^–3/2, respectively). The energy content of the AE waveforms of transverse specimens were greater than those of the longitudinal specimens implying higher fracture resistance in the transverse crack growth direction. The results showed that the propagation of the main crack involved weakening of the tissue by ultrastructural (diffuse) damage at the fracture plane and formation of linear microcracks away from the fracture plane for the transverse specimens. For the longitudinal specimens, the growth of the main crack occurred in the form of separations at lamellar interfaces. The lamellar separations generally arrested at the cement lines. Linear microcracks occurred primarily in the interstitial tissue for both crack growth directions.     

A fracture mechanics and mechanistic approach to the failure of cortical bone

The fracture of bone is a health concern of increasing significance as the population ages. It is therefore of importance to understand the mechanics and mechanisms of how bone fails, both from a perspective of outright (catastrophic) fracture and from delayed/time‐dependent (subcritical) cracking. To address this need, there have been many in vitro studies to date that have attempted to evaluate the relevant fracture and fatigue properties of human cortical bone; despite these efforts, however, a complete understanding of the mechanistic aspects of bone failure, which spans macroscopic to nanoscale dimensions, is still lacking. This paper seeks to provide an overview of the current state of knowledge of the fracture and fatigue of cortical bone, and to address these issues, whenever possible, in the context of the hierarchical structure of bone. One objective is thus to provide a mechanistic interpretation of how cortical bone fails. A second objective is to develop a framework by which fracture and fatigue results in bone can be presented. While most studies on bone fracture have relied on linear‐elastic fracture mechanics to determine a single‐value fracture toughness (e.g., K_c or G_c), more recently, it has become apparent that, as with many composites or toughened ceramics, the toughness of bone is best described in terms of a resistance‐curve (R‐curve), where the toughness is evaluated with increasing crack extension. Through the use of the R‐curve, the intrinsic and extrinsic factors affecting its toughness are separately addressed, where ‘intrinsic’ refers to the damage processes that are associated with crack growth ahead of the tip, and ‘extrinsic’ refers to the shielding mechanisms that primarily act in the crack wake. Furthermore, fatigue failure in bone is presented from both a classical fatigue life (S/N) and fatigue‐crack propagation (da/dN) perspective, the latter providing for an easier interpretation of fatigue micromechanisms. Finally, factors, such as age, species, orientation, and location, are discussed in terms of their effect on fracture and fatigue behaviour and the associated mechanisms of bone failure.     

Fracture behaviour of chemical vapour deposited and hot isostatically pressed zinc sulphide ceramics

Fracture behaviour of zinc sulphide ceramics prepared by chemical vapour deposition (CVD) followed by hot isostatic pressing (CVD + HIP) was investigated in terms of flexural strength (σ_f), plane-strain fracture toughness (K_Ic), even conditional fracture toughness (K_IQ), R-curve behaviour (variation of total fracture energy release rate, J_c with crack extension, δ/δ_c) and fracture mode. The corresponding Knoop Hardness number (KHN) and its correlations to flexural strength (σ_f) are also evaluated and reported. The present study showed that the zinc sulphide (ZnS) ceramics processed by CVD exhibited higher fracture resistance compared to ZnS processed by CVD + HIP condition. This observation is principally attributed to higher grain size associated with post-CVD HIPing process. In both conditions, the ZnS materials exhibited conditional fracture toughness (K_IQ) that decreased moderately with increased crack length due to the change in fracture mode form grossly tensile to predominant shear. A constantly rising R-curve behaviour was indicated in both the materials with significant increase in total fracture energy release rate (J_c with the normalised displacement (δ/δ_c), a parameter representing crack extension.     

Notch fracture toughness of high-strength Al alloys

In this study, the notch fracture toughness (NFT) of high-strength Al alloys was examined by a non-standardized procedure. The NFT is defined as the critical notch stress-intensity factor (NSIF) K_ρ,c, which is determined by using several methods of analysis and computing. A set of specimens with different notch root radii made from overaged 7xxx alloy forging was selected. The influence of the notch radius on the fracture toughness of the material was considered. It was found that the notch radius strongly affects the fracture behavior of forged 7xxx alloy in overaged condition. The notch fracture toughness was higher than the fracture toughness of a cracked specimen and increased linearly with notch radius. The critical notch radius was related to the spacing of intermetallic (IM) particles which promote an intergranular or transgranular fracture mechanism according to their size. It appeared that ductile transgranular fracture generated by the formation of dimples around dispersoids and matrix precipitates was predominant which indicates that intense strains are limited to a much smaller zone than the coarse IM particles spacing. This double mechanism is also operate for crack propagation of ductile fatigue. The nature and morphology of IM particles exert significant effects on the rate of fatigue crack growth and fracture toughness properties.     

Interlaminar and intralaminar fracture modes in 0/90 cross-ply glass/epoxy laminate

Delamination of a cross-ply 0/90 glass fibre-reinforced composite laminate with an epoxy-phenol matrix was studied using a double cantilever beam test. Fracture toughness was determined by measurement of bend angle of the cantilever beams. Results obtained with this method were in agreement with those from conventional compliance and area methods. Two different fracture modes were observed: interlaminar and intralaminar. In the interlaminar fracture mode, crack jumps in the space between two neighbouring 0° and 90° plies were observed. With the interlaminar fracture mode, during crack initiation G_Ic decreased with crack length. Intralaminar fracture mode consisted of the gradual growth of a crack through a 0° ply. Fibres bridging the opposite sides of the crack were observed in this case, and fracture toughness G_Ic did not change with crack length. G_Ic (420 J m⁻²) at intralaminar fracture mode was approximately twice that at interlaminar fracture mode (220 J m⁻²). The difference in fracture toughness was explained by the dissipation of energy by fibres bridging the opposite sides of the crack at intralaminar fracture mode.     

Estimation and comparative study of JIC using different methods for 20MnMoNi55 steel

Fracture toughness is one of the key input variables to compute critical load of the structural components. The resistance against ductile fracture can be quantified either by the initiation value or by the entire resistance curve. Different standard methods like J_SZW, JSME and ASTM: E1820 etc. are mainly used to estimate the critical crack initiation value from the resistance curve developed by the J-integral test. However, the results vary from method to method and are even inconsistent for the same method. Pehrson and Landes suggested a simple method for estimation of the critical fracture toughness by identifying the critical point corresponding to the maximum load on load–displacement curve. In the present study, different standard methods along with the one suggested by Pehrson and Landes are used to find out the critical fracture toughness using 1T–CT and ½T–CT specimens of the material 20MnMoNi55 steel for varying temperatures and crack size. The results are analyzed to compare the merits of the different methods of estimation of fracture toughness.     

Toughness of glass fibres reinforced glass-ionomer cements

Two fracture toughness parameters, the critical stress intensity factor, K _c and the work of fracture, W _f have been used to characterise the toughness of conventional and resin-modified glass-ionomer cements reinforced with glass fibres. The critical stress intensity factor was determined from the peak load, and the work of fracture was determined as the energy required to extend an introduced crack through the respective glass ionomers. For both materials, crack propagation became more stable as the weight fraction of glass fibres was increased. Additionally, when the weight percent of glass fibres was increased the work of fracture increased. Fibre bridging at the crack tip resulted in the increase in the work of fracture. As the percentage weight of fibres was increased, the critical stress intensity factor decreased proportionally to the increase in porosity.     

The true toughness of human cortical bone measured with realistically short cracks

Bone is more difficult to break than to split. Although this is well known, and many studies exist on the behaviour of long cracks in bone, there is a need for data on the orientation-dependent crack-growth resistance behaviour of human cortical bone that accurately assesses its toughness at appropriate size scales. Here, we use in situ mechanical testing to examine how physiologically pertinent short (<600 microm) cracks propagate in both the transverse and longitudinal orientations in cortical bone, using both crack-deflection/twist mechanics and nonlinear-elastic fracture mechanics to determine crack-resistance curves. We find that after only 500 microm of cracking, the driving force for crack propagation was more than five times higher in the transverse (breaking) direction than in the longitudinal (splitting) direction owing to major crack deflections/twists, principally at cement sheaths. Indeed, our results show that the true transverse toughness of cortical bone is far higher than previously reported. However, the toughness in the longitudinal orientation, where cracks tend to follow the cement lines, is quite low at these small crack sizes; it is only when cracks become several millimetres in length that bridging mechanisms can fully develop leading to the (larger-crack) toughnesses generally quoted for bone.     

Hydrogen permeability of niobium during cathodic polarization in hydrochloric acid

Conclusions For high-strength chilled steel, the limit value of the stress intensity factor K^IIIp attained in antiplane strain during short-period fracture by shear is a characteristic that is not sensitive to the effect of an ambient medium such as water and aqueous solutions of sulfuric acid. The possible reduction of short-period bearing capacity of specimens with a crack during loading by mode III takes place only as a consequence of reorientation of the crack into the plane in which the maximum normal stresses act and is associated with reduction in fracture toughness during tear (K_1c) because of the effect of the medium.During long-term corrosion tests in antiplane strain of specimens with a crack, the final act of fracture is almost always completed by tear. In addition, preceding spontaneous fracture, subcritical crack growth is possible by both tear and shear. For certain structural states of steel and ambient media, the latter mechanism and the corresponding high rate of subcritical crack growth may become dominant at low levels of K^III0. This explains the anomalous character of curves of long-term crack resistance observed in these cases.Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 13, No. 1, pp. 42–46, January–February, 1977.     

Micro-crack initiation at tip of a rigid line inhomogeneity in piezoelectric materials

For the square-root singularity shear stress found at the tip of a rigid line inhomogeneity (an anti-crack) in piezoelectric media, one possible way of releasing high strain energy is to initiate a micro-crack at the inhomogeneity tip. In our current study, a dislocation pileup model for micro-crack initiation at the inhomogeneity tip is proposed based on Zener-Stroh crack initiation mechanism. An interesting and important physical result that emerges from the analysis is that the critical stress intensity factor for the anti-crack (the line inhomogeneity) can be related to the fracture toughness of a conventional Griffith crack in the same material. Analytical results further show that under mechanical loading, the critical stress and electric displacement intensity factors of an anti-crack are only related to the corresponding intensity factors of stress and electric displacement of the crack, respectively. While if the anti-crack is under displacement loading (with net dislocation pile-up at the inhomogeneity tip), the critical stress and electric displacement intensity factors of an anti-crack depend on both of the total mechanical dislocations b_T and electricity dislocations b_D.     

Fracture mechanical properties in controlled rolled CMn thermomechanically treated steels with splittings

Fracture mechanical properties of a thermomechanically treated CMn steel were investigated in both longitudinal and transverse directions relative to the rolling direction. The CTOD fracture toughness testing was performed at three deformation rates in the temperature range from −60 to +40°C. Fracture initiation was investigated at room temperature. The CTOD fracture toughness depended very much on the specimen orientation with respect to sulphide inclusions. In the transverse specimens, maximum load was reached just after yielding, hence the recorded CTOD_m values were nearly independent of the rate of deformation and testing temperature.