Size effects and ductile-brittle transition of polypropylene

The influence of specimen width on fracture parameters has been investigated. The range examined was sufficiently large to obtain ductile and brittle fractures. With reference to previously published work, the phenomenology has been analysed by combining BCS model and Carpinteri's brittleness number approach.Nomenclature a crack length - f(a/W) shape function according to ASTM specification [16] - F(a/W) shape function according to Tada Paris notation [21] - E elastic modulus - K _IC plane strain fracture toughness - K _IC ^f fictitious plane strain fracture toughness - K _IC2 plane stress fracture toughness - J _IC ^f J-integral at maximum load - L span - weight average molecular weight - number average molecular weight - polydispersity - P _M maximum load - P _F load of brittle fracture - p _P load of plastic collapse - s brittleness number - V machine cross speed - W specimen width - _y yield stress - strain rate     

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.     

Study on the behavior of elastic-plastic fracture under mixed I+II mode loading in aluminum alloy Ly12-J-integral analysis

The elastic-plastic fracture behavior of aluminum alloy Ly12 under mixed I+II mode loading was studied by finite element method and fracture test. A mixed mode elastic-plastic fracture criterion of J-integral was proposed by using the J-resistance curve, and the maximum fracture effective plastic strain _p max of different mixed ratios at crack tip were also calculated. The results show that(1) the initiation J-integral values of different mixed ratios have the equation

Effects of thickness and environmental temperature on fracture behaviour of polyetherimide (PEI)

The fracture behaviour of a polyetherimide (PEI) thermoplastic polymer was studied using compact tension (CT) specimens with a special emphasis on effects of specimen thickness and testing temperatures on the plane strain fracture toughness. The results show that the valid fracture toughness of the critical stress intensity factor, K _IC, and strain energy release rate, G _IC, is independent of the specimen thickness when it is larger than 5 mm at ambient temperature. On the other hand, the fracture toughness is relatively sensitive to testing temperatures. The K _IC value remains almost constant, 3.5 MPa in a temperature range from 25 to 130°C, but the G _IC value slightly increases due to the decrease in Young's modulus and yield stress with increasing temperature. The temperature dependence of the fracture toughness, G _IC, was explained in terms of a plastic deformation zone around the crack tip and fracture surface morphology. It was identified that the larger plastic zone and extensive plastic deformation in the crack initiation region were associated with the enhanced G _IC at elevated temperatures.     

Investigation of the Fracture of Brittle Bodies Due to Their Contact Interaction with Rigid Dies

We propose a theoretical and experimental procedure for determining fracture conditions of brittle bodies subjected to the action of rigid dies of various shapes. Similarly to the fracture mechanics approach, we specify the stress intensity factors K₁ and K₂ in the vicinity of the die base, which determine the conditions of crack initiation, as well as values of the angle between cracks and the specimen base. It is established that upon the specimen compression by the die, the angle of the inclination of the fracture surface to the specimen base plane remains practically unchanged , which agrees fairly well with the theoretical data obtained. Body fragments have been revealed after pressing dies of different types into specimens: in a shape close to a circular cone for a round die, in a shape close to a quadrangular pyramid for a square die, and in a shape close to a triangular prism for a rectangular die.     

Unified correlation of in‐plane and out‐of‐plane constraints with fracture toughness

In this paper, the specimens with different geometries and loading configurations were used to study the unified correlation of in‐plane and out‐of‐plane constraints with fracture toughness by using numerical simulation method. The results show that the unified constraint parameter A_p which was defined on the basis of the areas surrounded by the equivalent plastic strain isolines ahead of crack tip can characterise both in‐plane and out‐of‐plane constraints induced by different specimen geometries and loading configurations. A sole linear relation between the normalised fracture toughness J_IC/J_ref and was obtained. The J_IC/J_ref ‐ line is a unified correlation line of in‐plane and out‐of‐plane constraints with fracture toughness of a material, and the constraint dependent fracture toughness of a material can be determined from the unified correlation line. The results also demonstrate that the out‐of‐plane constraint effect is related to the in‐plane constraint effect, and there exists interaction between them. The higher in‐plane constraint strengthens the out‐of‐plane constraint effect, whereas the lower in‐plane constraint is not sensitive to the out‐of‐plane constraint effect.     

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.     

A numerical study on the crack tip constraint of pipelines subject to extreme plastic bending

This study investigates the fracture response and crack tip constraint of thick wall pipelines subject to large plastic bending. Such a circumstance frequently occurs during the installation of offshore pipelines (such as the reeling method), and accidental overloading, both inducing inelastic bending. The near-tip stress and strain fields are obtained through the fully nonlinear 3D finite element models constructed to examine the response of a practical range of cracked pipeline geometries and material properties. It is observed that throughout the loading history (up to the large scale yielding of the pipeline), by incorporation of the J–Q two parameter fracture theory, the near crack tip fields do indeed resemble those obtained from a K–T modified boundary layer formulation. This analogy provides sufficient proof for the applicability of the similitude concept inherent and fundamental to any fracture assessment procedure. All the pipelines considered in this study, which had realistic crack sizes, exhibited low constraint behavior (i.e. −1.4 < Q < −0.4). Additionally, Q was observed to decrease as a linear function of the global bending strain. Based on this correlation, simplified design equations are presented by which the constraint of such pipelines could be effectively estimated. The equations would be suitable for incorporation in the constraint-matched integrity assessment procedures that would in turn overcome the overt conservatism produced by the use of single parameter fracture mechanics approaches. Suitability of the low constraint laboratory specimens for fracture toughness measurements is also confirmed.     

Unified characterisation of in‐plane and out‐of‐plane constraint based on crack‐tip equivalent plastic strain

Constraint can be divided into two conditions of in‐plane and out‐of‐plane, and each of them has its own parameter to characterize. However, in most cases, there exists a compound change of both in‐plane and out‐of‐plane constraint in structures, a unified measure that can reflect both of them is needed. In this paper, the finite element method (FEM) was used to calculate the equivalent plastic strain (ɛ_p) distribution ahead of crack tips for specimens with different in‐plane and out‐of‐plane constraints, and the FEM simulations based on Gurson–Tvergaard–Needleman (GTN) damage model and a small number of tests were used to obtain fracture toughness for the specimens with different constraints. Unified measure and characterisation parameter of in‐plane and out‐of‐plane constraints based on crack‐tip equivalent plastic strain has been investigated. The results show that the area A_PEEQ surrounded by the ɛ_p isoline ahead of crack tips can characterize both in‐plane and out‐of‐plane constraints. Based on the area A_PEEQ, a unified constraint characterisation parameter A_p was defined. It was found that there exists a sole linear relation between the normalised fracture toughness J_IC/J_ref and regardless of the in‐plane constraint, out‐of‐plane constraint and the selection of the ɛ_p isolines. The unified J_IC/J_ref−reference line can be used to determine constraint‐dependent fracture toughness of materials. The FEM simulations with the GTN damage model (local approach) can be used in obtaining the unified J_IC/J_ref−reference line for materials with ductile fracture.     

Experimental and numerical investigation of cracked chevron notched Brazilian disc specimen for fracture toughness testing of rock

The cracked chevron notched Brazilian disc (CCNBD) specimen has been suggested by the International Society for Rock Mechanics to quantify mode I fracture toughness (K_Ic) of rock, and it has also been applied to mode II fracture toughness (K_IIc) testing in some research on the basis of some assumptions about the crack growth process in the specimen. However, the K_Ic value measured using the CCNBD specimen is usually conservative, and the assumptions made in the mode II test are rarely assessed. In this study, both laboratory experiments and numerical modeling are performed to study the modes I and II CCNBD tests, and an acoustic emission technique is used to monitor the fracture processes of the specimens. A large fracture process zone and a length of subcritical crack growth are found to be key factors affecting the K_Ic measurement using the CCNBD specimen. For the mode II CCNBD test, the crack growth process is actually quite different from the assumptions often made for determining the fracture toughness. The experimental and numerical results call for more attention on the realistic crack growth processes in rock fracture toughness specimens.     

Prediction of Fracture Toughness of Reactor Pressure-Vessel Steels Using the “Master Curve” Concept and Probabilistic Model

Using a probabilistic model and the Master curve approach, the temperature dependence of the brittle fracture toughness of reactor pressure-vessel steel 15Kh2NMFA in the initial state and highly embrittled state is predicted from the results of fracture toughness testing of a cracked Charpy-type specimen at a given temperature. A comparative analysis has shown that for the steel in the initial state the curves calculated by the probabilistic model and by the Master-curve approach are in good agreement. By testing compact-tension specimens of embrittled 2T-CT steel in a wide temperature range the authors have obtained experimental fracture toughness values and compared them with the calculated curves. It is demonstrated that, in the case of the embrittled steel, the curve as calculated by the Master-curve approach fails to describe adequately the experimental results, while the curves plotted by the probabilistic model agree well with the experimental fracture toughness values.     

J–R curves corrected by load-independent constraint parameter in ductile crack growth

The constraint effect on J–resistance curves of ductile crack growth is considered under the condition of two-parameter J–Q^* controlled crack growth, where Q^* is a modified parameter of Q in the J–Q theory. Both J and Q^* are used to characterize the J–R curves with J as the loading level and Q^* as a constraint parameter. It is shown that Q^* is independent of applied loading under large-scale yielding or fully plastic deformation, and so Q^* is a proper constraint parameter during crack growth. An approach to correct constraint effects on the J–R curve is developed, and a procedure of transferring the J–R curves determined from standard ASTM procedure to nonstandard specimens or real cracked structures is outlined.The test data of fracture toughness, J_IC, and tearing modulus, T_R, by Joyce and Link (Engng. Fract. Mech. 57(4) (1997) 431) for a single-edge notched bend specimen with various depth cracks are employed to demonstrate the efficiency of the present approach. The variation of J_IC and T_R with the constraint parameter Q^* is obtained, and then a constraint-corrected J–R curve is constructed for the test material of HY80 steel. Comparisons show that the predicted J–R curves can match well with the experimental data for both deep and shallow cracked specimens over a reasonably large amount of crack extension.Finally, the present approach is applied to predict the J–R curves of ductile crack growth for five conventional fracture specimens. The results show that the effect of specimen geometry on the J–R curves is generally much larger than the effect of specimen sizes, and larger specimens tend to have lower crack growth resistance curves.     

Three‐dimensional analyses of in‐plane and out‐of‐plane crack‐tip constraint characterization for fracture specimens

Three‐dimensional elastic–plastic finite element analyses have been conducted for 21 experimental specimens with different in‐plane and out‐of‐plane constraints in the literature. The distributions of five constraint parameters (namely T‐stress, Q, h, T_z and A_p) along crack fronts (specimen thickness) for the specimens were calculated. The capability and applicability of the parameters for characterizing in‐plane and out‐of‐plane crack‐tip constraints and establishing unified correlation with fracture toughness of a steel were investigated. The results show that the four constraint parameters (T‐stress, Q, h and T_z) based on crack‐tip stress fields are only sensitive to in‐plane or out‐of‐plane constraints. Therefore, the monotonic unified correlation curves with fracture toughness (toughness loci) cannot obtained by using them. The parameter A_p based on crack‐tip equivalent plastic strain is sensitive to both in‐plane and out‐of‐plane constraints, and may effectively characterize both of them. The monotonic unified correlation curves with fracture toughness can be obtained by using A_p. In structural integrity assessments, the correlation curves may be used in the failure assessment diagram (FAD) methodology for incorporating both in‐plane and out‐of‐plane constraint effects in structures for improving accuracy.     

A methodology for measuring interface fracture properties of composite materials

A methodology is presented for measuring interface fracture properties of composite materials. A bimaterial Brazilian disk specimen with a crack along the interface is employed. The specimen is analyzed by means of the finite element method and a conservative integral to determine stress intensity factors as a function of loading angle and crack length. A weight function is employed to determine the effect of residual curing stresses on the stress intensity factors. These are combined to determine the critical interface energy release rate _ic as a function of stress intensity phase angle for tests carried out on a glass/epoxy material pair.     

Short-rod elastic-plastic fracture toughness test using miniature specimens

The standard ASTM-E399 plane-strain fracture toughness (K _IC) test requires (1) the test specimen dimensions to be greater than a minimum size and, (2) fatigue precracking of the specimen. These criteria render many materials impractical to test. The short-rod elastic-plastic plane-strain fracture toughness test proposed by Barker offers a method of testing not requiring fatigue precracking and furthermore, it appears that test specimens smaller than that stipulated by ASTM can be used to obtain validK _IC values. In this study, the use of a modified miniature short-rod fracture toughness test specimen was investigated. Our miniature short-rod specimen is approximately 7 mm long and 4 mm diameter. These mini specimens are well suited for the purpose of testing biomaterials. The value of the minimum stress intensity factor coefficient (Y _m ^* ) for the mini short-rod specimens was determined experimentally using specimens machined from extruded acrylic rod stock. An elastic-plastic fracture toughness analysis using the mini specimens gave values ofK _IC for extruded acrylic (nominally PMMA) equal to 0.67 ± 0.06 MPa m^1/2. The problem of testing non-flat crack growth resistance curve materials (such as PMMA) using the short-rod fracture toughness test method is discussed. A modification to the test procedure involving the use of aY ^* value corresponding to a short crack length is suggested as a method of overcoming this difficulty.Nomenclature a crack length - a ₀ initial crack length - a ₁ length of the chevron notch on the mini short-rod specimen - a _m critical crack length — crack length atY _m ^* - C specimen compliance - C dimensionless specimen compliance = CED - D mini short-rod specimen diameter - E Young's modulus - K ₁ stress intensity factor - K _1C plane-strain fracture toughness - K _max fracture toughness calculated usingP _max - P load applied to the test specimen during a short-rod fracture toughness test - P _c load applied to the test specimen atY _m ^* - P _max maximum load applied to the specimen during a short-rod fracture toughness test - p plasticity factor - W mini short-rod specimen width - Y ^* stress intensity factor coefficient - Y _m ^* minimum of the stress intensity factor coefficient - dimensionless crack length =a/W - ₀ dimensionless initial crack length = ₀/W - ₁ dimensionless chevron notch length =a ₁/W - _m dimensionless critical crack length =a _m/W     

Crack-tip constraint in mode II deformation

Studies of cracked specimens loaded in mode I have shown that the stresses near the crack tip depend significantly on the level of constraint. The stresses can be determined near the crack tip using the HRR solution, but only for high constraint specimens. For other levels of constraint, O'Dowd and Shih's Q parameter may be used to adjust the stresses derived from the HRR solution. Only limited research has been carried out to study the effect of constraint in mode II. In this paper a mode II boundary layer formulation is used to study the effect of far field elastic stresses on the size and shape of the plastic zone around the crack tip and on the stresses inside the plastic zone. It is shown that in mode II, both positive and negative values of remote T-stress influence the tangential stress along the direction of maximum tangential stress. In the spirit of O'Dowd and Shih, a dimensionless parameter Q _II is introduced to quantify the constraint for mode II specimens failing by brittle fracture. The relation between Q _II and T/₀ is determined for different values of the strain hardening coefficient n. To investigate the range of validity of the Q–T diagram for real specimens, the constraint parameter Q _II is calculated directly from finite element analysis for three mode II specimens and compared with the evaluation using the Q–T diagram.     

Fracture toughness and fracture mechanisms of PBT/PC/IM blend

The static and impact fracture toughnesses of a polybutylene terephthalate/polycarbonate/impact modifier (PBT/PC/IM) blend were studied at different temperatures. The static fracture toughness of the blend was evaluated via the specific fracture work concept and the J-integral analysis. A comparison of these two analytical methods showed that the specific essential fracture work, W _e, was equivalent to the obtained by the ASTM E813-81 procedure, representing the crack initiation resistance of the material. The discrepancy between W _e and of ASTM E813-89 was caused by the extra energy component in consumed by a 0.2 mm crack growth. Impact fracture toughness was also analysed using the specific essential fracture work approach. When the fracture was elastic, W _e was equivalent to the critical potential energy release rate, G _IC, obtained via LEFM analysis. Temperature and strain-rate effects on the fracture toughness were also studied. The increase in impact toughness with temperature was attributed to two different toughening mechanisms, namely, the relaxation processes of the rubbery particles and the parent polymers in a relatively low-temperature range and thermal blunting of the crack tip at higher temperatures. The enhancement in static fracture toughness at temperatures below — 60 °C was thought to be caused by plastic crack-tip blunting, but the monotonic reduction in yield stress was largely responsible for the toughness decreasing with higher temperatures. The temperature-dependent fracture toughness data obtained in static tests could be horizontally shifted to match roughly the data for the impact tests, indicating the existence of a time-temperature equivalence relationship.     

Enhancement of the Crack Resistance of Manganese Cast Irons

We have determined the parameters of static and cyclic crack resistance of austenitic manganese irons . The results obtained were compared with literature data. High K _IC values in the alloys under consideration were reached owing to the refining action of calcium. We have studied the micromechanism of fracture of these materials with the use of modern methods of investigation. We have shown that the parameters of the graphitic phase as well as the toughness and plasticity of the metal matrix affect the breaking strength significantly.__________Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 41, No. 1, pp. 63 – 68, January – February, 2005.     

The effect of initial notch shape of compact specimen on fatigue pre-cracking and fracture toughness testing

The circular notched compact specimens, along with standard specimens having straight or chevron notch are provided for fatigue and fracture toughness testings in order to study the crack observation capability during fatigue pre-cracking, skewness of the crack front, and the resulting fracture toughness K_Q. The test results indicated that circular notched specimens significantly facilitate the crack observation during fatigue testing as the cracks initiate on both surfaces of the specimen. No remarkable differences were observed on geometries of the fatigue crack front obtained and the resulting fracture toughness among these three types of specimen. The macroscopic observation of beach marks on the fracture surfaces revealed that, in the present material Ti-6Al-4V (ELI), the advance of only 1.3% of the whole crack length corresponded to the load level at which fracture toughness K_Q was evaluated.     

Measurement of mode I and mode II rock dynamic fracture toughness with cracked straight through flattened Brazilian disc impacted by split Hopkinson pressure bar

In order to find an effective and convincing method to measure rock dynamic fracture toughness for mode I and mode II, cracked straight through flattened Brazilian disc specimens of marble, which were geometrically similar for three size, were diametrically impacted by split Hopkinson pressure bar on the flat end of the specimen with three load angle respectively. History of stress intensity factors (K_I(t) for opening mode I, and K_II(t) for sliding mode II), mode mixture ratio (K_I(t)/K_II(t)), as well as mode I and mode II dynamic fracture toughness at crack initiation (K_Id and K_IId) were determined with the experimental–numerical method. It is found that there is a unique size effect for dynamic fracture test with the specimens, the mode mixture ratio is not solely determined by load angle (the angle between load direction and crack line) as in the static loading; the pure mode II load angle is 19° for the ?50 mm specimen, however it is 10° for the ?130 mm and ?200 mm specimens; the mode II load angle decreases with increment of specimen size. Realization of pure mode II is justified by the mode mixture ratio approaching zero, it can be realized under certain load angle and loading rate for the specimen of specified size. K_IId is generally greater than K_Id. Both K_Id and K_IId increase with increment of specimen size, and this trend for K_IId is more remarkable than that for K_Id.