Effect of stress wave propagation phenomenon on the determination of strain energy density theory parameters and dynamic J-integral

Dynamic loading for stationary cracks leads to results that are many times greater in magnitude than their static counterparts. If the dynamic loading is in the form of impact type, stress wave propagation effects become dominant. FRAC3D program comprises enriched element formulation which doesn't require excessive mesh refinement around crack tip for accuracy. Strain energy density (SED) theory parameters and dynamic J-integral are sought in this study to simulate and understand wave propagation phenomenon in detail. Structures under the effect of wave propagations yield more reliable J-integral values by taking the average of the results from multiple domain sizes. Governed by stress waves, space-time variations of minimum energy density locations strongly influence fracture characterization for straight and curved crack fronts. Details given in numerical examples section of this paper make a great contribution to understanding of the response for cracked structures subjected to sudden loading.     

Modeling of the fracture of elasticoplastic materials capable of undergoing a phase transition

An investigation was made of the fracture of a layer of iron undergoing a polymorphic α-ε phase transition caused by a detonation wave, using an elasticoplastic model of the deformation of a continuous medium with spallation. The influence of the elastic precursor on the spallation was identified. Pis’ma Zh. Tekh. Fiz. 24, 91–95 (September 26, 1998)     

Size effect on the contact state between fracture specimen and supports in Hopkinson bar loaded fracture test

To thoroughly understand the dynamic behavior of a fracture specimen under stress wave loading, dynamic fracture test with various three-point bend (3PB) specimens are performed on the Hopkinson bar loaded experimental apparatus. The contact state between the fracture specimen and supports during the loading process is examined via stress wave propagation analysis. The experimental results show that the fracture specimen with usual dimensions does not keep contact with supports in the initial loading stage, i.e. a loss of contact phenomenon occurred. The specimen dimensions and the span of the loading apparatus are important factors affecting specimen’s contact state. The loss of contact is more obvious with increasing span under the same specimen dimensions. Conversely, the loss of contact gradually disappears with increasing specimen length or increasing width under a fixed span. Based on experimental investigations, a criterion is established to ensure the fracture specimen keep in contact with supports during dynamic fracture test.     

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.     

爆破载荷下隧道围岩破坏裂隙范围研究

为确定爆破载荷作用下岩体的裂隙范围，应用摩尔-库伦强度准则确定岩石在冲击波作用下的粉碎区；在考虑粉碎区范围、应力波衰减指数改变和岩石三向受力状态的情况下,用Mises强度准则计算裂隙区范围；在不考虑爆生气体在应力波形成的裂隙区损失的前提下，用岩石的断裂韧性来计算爆生气体充满粉碎区后岩石裂隙的二次扩展范围。通过理论计算与现场声波实测值对比，理论计算值比实测值小8.45%。分析表明，该裂隙范围计算方法合理，并可以对类似工况的裂隙范围进行估算。     

Analysis of pipeline fracture by fast crack propagation

An analysis is presented of the influence of wave processes in gases and in a pipeline wall on extended fracture by fast crack propagation. The influence of design and technological parameters of the pipeline and of the pipe metal fracture toughness on the extent of fracture is shown. Translated from Problemy Prochnosti, No. 2, pp. 119–125, March, 1997.     

Estimation of fracture energy from the work of fracture and fracture surface area: I. Stable crack growth

Past attempts to determine fracture energy by the work of fracture (γ _WOF) technique, in most cases, have resulted in greater estimates due to the use of the cross-sectional area rather than the actual area of the fracture surface in calculations. The actual fracture surface area A _F of soda-lime-silica glass chevron-notch flexure specimens was estimated using atomic force microscopy. An equation for A _F was developed using the data from these tests. The use of A _F in the equation for γ _WOF resulted in γ _WOF values less than values reported from traditional fracture mechanics tests and from those obtained using the cross-sectional area. The implication is that the tortuosity of the fracture surface contributes to the energy expended during fracture and should be accounted for in the calculation of the fracture energy. These calculations provide an estimate for the minimum energy required to break bonds in the fracture process.     

A review of the J and I integrals and their implications for crack growth resistance and toughness in ductile fracture

The application of the J and the I-integrals to ductile fracture are discussed. It is shown that, because of the finite size of the fracture process zone (FPZ), the initiation value of the J-integral is specimen dependent even if the plastic constraint conditions are constant. The paradox that the I-integral for steady state elasto-plastic crack growth is apparently zero is examined. It is shown that, if the FPZ at the crack tip is modelled, the I-integral is equal to the work performed in its fracture. Thus it is essential to model the fracture process zone in ductile fracture. The I-integral is then used to demonstrate that the breakdown in applicability of the J-integral to crack growth in ductile fracture is as much due to the inclusion in the J-integral of progressively more work performed in the plastic zone as it is to non-proportional deformation during unloading behind the crack tip. Thus J _R -curves combine the essential work of fracture performed in the FPZ with the plastic work performed outside of the FPZ. These two work terms scale differently and produce size and geometry dependence. It is suggested that the future direction of modelling in ductile fracture should be to include the FPZ. Strides have already been made in this direction.     

High speed double torsion tests on tough polymers. I: Linear elastic steady state and dynamic analysis

The High Speed Double Torsion test has been used to generate steady rapid crack propagation in tough pipe-grade polyethylenes, at speeds of up to 350 ms^-1. Dynamic plane-strain fracture resistance GD data, computed from the measured displacement and crack length using a linear elastic steady-state analysis, were systematically scattered. The computed fracture loads exceeded measured values by up to 50 percent. Two possible reasons for these discrepancies are the neglect of unsteady deformation, and the use of small-strain dynamic elastic modulus data to represent the material. Since the torsional wave speed calculated from this modulus provided a good estimate for the limiting crack speed, this paper pursues the first possibility. High speed photography was used to study the deformation field, which proved to be less steady than assumed. The observations were used to support development of a fully dynamic, linear elastic torsion-beam-on-elastic-foundation model for computing the transient deformation field from boundary data. The foundation stiffness, computed by matching predicted and observed deformations in the crack tip vicinity, was consistent with that estimated from earlier quasi-static tests. As judged by the continuity of the computed energy release rate G ^dyn (and hence, equivalently, of GD), numerical integration along characteristics is more suitable than a conventional explicit finite difference scheme for solving this one-dimensional problem. The GD solution for intermediate crack lengths is also insensitive to assumed initial conditions, which are therefore chosen to minimise the settling time. The curved double-torsion crack front shape, predicted using an earlier quasi-static criterion, agrees closely with that observed from dynamic arrest lines on the fracture surface, but simply assuming the crack front to be straight and normal to the specimen plane has little effect on computed GD data. The dynamic model, used to compute GD as a function of crack speed for several pipe-grade polyethylenes, reduces but does not eliminate scatter; nevertheless, in provides a more reliable and versatile tool for reconsidering the question of material representation in Part II of the paper.     

Intersonic shear crack growth along weak planes

Classical dynamic fracture theories predict the Rayleigh surface wave speed (c _R ) to be the limiting speed of propagation for mode-I cracks in constitutively homogeneous, isotropic, linear elastic materials subjected to remote loading. For mode-II cracks, propagating along prescribed straight line paths, the same theories, while excluding the possibility of crack growth in the speed regime between c _R and the shear wave speed, c _s , do not exclude intersonic (c _s <υ<c _l ) crack tip speeds. In the present study, we provide the first experimental evidence of intersonic crack growth in such constitutively homogeneous and isotropic solids, ever recorded in a laboratory setting. Intersonic shear dominated crack growth, featuring shear shock waves, was observed along weak planes in a brittle polyester resin under far-field asymmetric loading. The shear cracks initially propagate at speeds just above c _s and subsequently accelerate rapidly to the longitudinal wave speed (c _l ) of the solid. At longer times, when steady state conditions are attained, they propagate at speeds slightly higher than √2–c _s . The experimental results compare well with existing asymptotic theories of intersonic crack growth, and the significance of the preferred speed of √2–c _s is discussed. Received: 13 September 1999 / Reviewed and occerted: 19 November 1999     

Monitoring of delamination onset and growth during Mode I and Mode II interlaminar fracture tests using guided waves

A delamination monitoring method was proposed to characterize Mode I and Mode II delamination onset in carbon fiber/epoxy (CF/EP) composite laminates through interrogation of guided waves activated and captured using piezoelectric actuators and sensors in a pitch–catch configuration. Mode I and Mode II interlaminar fracture tests were conducted using double cantilever beam (DCB) and end notch flexure (ENF) specimens to evaluate the proposed method. The changes in wave propagation velocity and wave magnitude (or attenuation), and the degree of waveform similarity between excitation and response signals, were calculated as delamination-sensitive wave parameters and plotted versus displacement recorded using a materials testing system. The kink points determined from wave parameter–displacement curves agreed well with the deviation from linearity (NL), visual observation (VIS) and maximum load (Max) points, which are often used in conventional methods for determining interlaminar fracture toughness. The propagation characteristics of the A₀ wave mode in a low frequency range were demonstrated to have high sensitivity to Mode I and in particular Mode II delamination onset in CF/EP composite laminates. It was concluded that the guided waves propagating in the DCB and ENF specimens were capable of determining Mode I and Mode II interlaminar fracture toughness, complementing current practices based on visual inspection or trivial interrogation using load–displacement curve alone.     

Dynamic and static fracture analyses of graphene sheets and carbon nanotubes

Dynamic and static fracture properties of Graphene Sheets (GSs) and Carbon nanotubes (CNTs) with different sizes are investigated based on an empirical inter-atomic potential function that can simulate nonlinear large deflections of nanostructures. Dynamic fracture of GSs and CNTs are studied based on wave propagation analysis in these nanostructures in a wide range of strain-rates. It is shown that wave propagation velocity is independent from strain-rate while dependent on the nanostructure size and approaches to 2.2 × 10⁴ m/s for long GSs. Also, fracture strain shows extensive changes versus strain-rate, which has not been reported before. Fracture stress is determined as 115 GPa for GSs and 122 GPa for CNTs which are independent from the strain-rate; in contrast to the fracture strain. Moreover, fracture strain drops at extremely high strain-rates for GSs and CNTs. These features are considered as capability of carbon nanostructures for reinforcing nanocomposites especially under impact loadings up to high strain-rates.     

Crack-growth criterion for dynamic brittle fracture

An approach to the solution of problems of the mechanics of brittle dynamic fracture, which is based on the energy principle and the principle of time separation, is proposed. A so-called wave criterion of fracture, which can be used to estimate dynamic crack growth in an elastic body, is formulated on the basis of these principles. A general procedure is described for this estimation, and a comparison is made between experimental and theoretical values of crack-growth rate in a rectangular bar in a plane stress state (PSS); this confirms the applicability of the developed approach for engineering calculations.Translated from Problemy Prochnosti, No. 2, pp. 12–18, February, 1994.     

Fracture Waves Revisited

Self-sustaining fracture waves hypothesized by Galin and Cherepanov (1966) have been observed in shock-compressed glasses and in Prince Rupert’s drops, but their speed did not correspond to the predicted value. This controversy is addressed in the present note. We now assume that this speed is equal to the local velocity of sound in the particulate material just behind the wave front, and show that, then, it is in a reasonable agreement with test data. The specific heat spent on the self-sustaining fracture wave in soda lime glass is estimated to be 1 to 20 J/g for moderately high pressures.     

Enhanced failure of ceramics irradiated by combined pulse and c.w. lasers

Several ceramic materials were subjected to the combined irradiation of a 1.06 pulse and a 10.6 continuous wave (c.w.) laser. The duration of c.w. irradiation required to cause failure from the combined exposure is compared to that from c.w. irradiation alone. For example, thin Pyroceram and soda-lime glass plates burned through when exposed to the c.w. laser followed by the single pulse laser, in about one half the time required to cause fracture during exposure to the c.w. laser alone. Also, enhanced catastrophic fracture of thick soda-lime glass plates resulted when the c.w. irradiation followed the pulse within 0.3 sec. Finally, the effects of the combined pulse and c.w. exposure are compared with the effects of single or multiple pulses, and the apparent enhancement is discussed in terms of beam size and power.The term ceramics in this paper refers to non-crystalline (glasses) as well as single and polycrystalline ceramics.     

Impact of particle packing mix design method on fracture properties of natural and recycled aggregate concrete

The fracture properties of four types of concrete prepared using natural coarse aggregate and recycled coarse aggregate and conventional and particle packing method (PPM) of mix design approaches are studied. The three‐point bending (TPB) test is performed using three different sizes of single edge notched beam. The fracture energy is calculated from the load‐CMOD curve obtained in the TPB test, and in this process the load‐CMOD curve is curtailed at 2% of the depth of the beam. Based on CTOD_c and w₁ relationship, appropriate softening function is used to estimate the double‐K fracture parameters. The fracture energy and fracture toughness parameters of recycled aggregate concrete (RAC) is inferior to the natural aggregate concrete (NAC). The PPM mix design improves the fracture properties of concrete in comparison to the conventional mix design approach. The fracture properties of PPM mix designed RAC are comparable to that of NAC prepared using conventional method.     

The Essential Work of Fracture (EWF) method – Analyzing the Post-Yielding Fracture Mechanics of polymers

The Post-Yielding Fracture Mechanics describe the fracture behaviour of pre-cracked films and thin sheets that show yielding phenomenon at the crack tip during fracture. The Essential Work of Fracture method (EWF) has been used for this type of fracture characterization, determining two parameters: the specific work of fracture, w_e related with the real fracture process area, and the specific non-essential work of fracture, w_p that corresponds with the work done in the outer region of the crack tip.The EWF technique has been successfully employed especially with polymers, allowing the study of the influence of many variables in fracture properties, unavailable using other techniques such us K_IC or J_IC determination. In this work, the fundamentals of the technique and examples of application are reviewed, presenting a brief summary of the most relevant contributions of our group to the EWF method.     

Deformation and fracture of cork in tension

Various properties related to the deformation and fracture of cork in tension were experimentally determined, including the Young's modulus, the stress and strain at fracture and the fracture toughnessK _Ic. The transverse isotropy of cork implies that there are three independent systems of mode I crack propagation andK _Ic was measured for each. The mechanisms of deformation and fracture were identified by SEM microscope observation ofin situ deformation and of the fracture surfaces and crack paths. Two fundamental mechanisms of fracture occur: crack propagation along the lateral cell walls in non-radial tension, withK _Ic = 94±16 kPam^1/2 and crack propagation by breaking the cell walls in radial tension withK _Ic=125±14 kPam^1/2. In radial tension, local fractures that do not propagate due to crack stopping were observed which lead to serrations in the tensile curves for that direction. The strain to fracture in this direction is considerably larger than in the perpendicular (non-radial) directions.     

Critical evaluation of indentation fracture toughness measurements with Vickers indenter on yttria‐stabilized zirconia dental ceramics

The purpose of this study was to investigate and analyze fracture toughness (K_Ic) of yttria stabilized tetragonal zirconia (Y‐TZP) dental ceramics by the Vickers indentation fracture test. In order to determine fracture toughness, the Vickers indenter was used under the load of 294.20 N (HV30). The cracks, which occur from the corners of a Vickers indentation, were measured and used for fracture toughness determination, through five mathematical models according to (I) Anstis, (II) Evans and Charles, (III) Tanaka, (IV) Niihara, Morena and Hasselman and (V) Lankford. Morphology of indentation cracking was determined by scanning electron microscope. The most adequate model for determination of fracture toughness (K_Ic) of yttria stabilized tetragonal zirconia dental ceramics by the Vickers indentation fracture test is Lankford model.     

Correlation between crack tortuosity and fracture toughness in cementitious material

This paper proposes a new technique for the evaluation of fractal dimension (D) of fracture surface and a quantitative correlation between D and fracture toughness of cementitious materials. The experimental program has been performed on compact tension (CT) specimens (600 × 525 × 125 mm) with three different aggregate sizes (d _max=4.7 mm, 18.8 mm and 37.5 mm). The fractal geometry concept is utilized in the evaluation of fracture surface roughness. To avoid indirect or destructive experimental procedures that are prohibitively laborious and time consuming, a new non-destructive technique is presented. Results of the analysis indicate that the concept of fractal geometry provides a useful tool in the fracture surface characterization. The results also suggest that the fracture toughness can be correlated with the fractal dimension of fracture surface.