Crack Resistance Curves Research Articles

Determination of Material Characteristic Values in Elastic-Plastic Fracture Mechanics by Means ofJ-Integral Crack Resistance Curves

AbstractThis article discusses the problem of determining the characteristic values in ductile fracture mechanics on the basis of the J-integral. Special interest is directed towards the question of transferability of the characteristic values from laboratory specimens to large-scale specimens of dimensions similar to those of components.For this purpose technical substitute values and physical crack initiation characteristic values were determined from a number of specimens and a wide range of materials, showing the effect of material toughness and specimen geometry on the characteristic values. Technical substitute values were determined per ASTM (JIc), Loss et al. (J0.15), and Schwalbe and Heerens (J0.2). Determination of the physical crack initiation value resulted from measurements of the stretched zone.The technical substitute values and the physical crack initiation values were compared with results for large-scale specimens. Only the physical crack initiation value (Ji) correctly described the behavior of large-scale specimens regarding crack initiation.

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.

Computer Simulations of R‐Curve Behavior in Microcracking Materials

A computer program has been developed which simulates the process of microcracking in two‐phase ceramic materials. This simulation provides a method of examining the complex interactions which occur between a propagating crack and the residually stressed particles around it. As the residual stresses near second‐phase inclusions are relieved by microcrack formation, a process zone forms around the main crack, partially shielding it. The resulting crack resistance curves, or R curves, associated with crack shielding mechanisms are generated by the program. Three variables— the microcrack density (fs), the dilatant strain associated with each microcracked particle (θ), and the orientation of the microcracks (Ψ)— were used to determine their influence on fracture toughness. The steady‐state toughness was found to increase with second‐phase particle additions, increased dilatant strain, and the formation of microcracks parallel to the direction of applied stress. However, the magnitude of toughening increase attained in these‐simulations was generally lower than that predicted by continuum models. This discrepancy is attributed to the fact that interactions between microcracks produce frontal zones which result in a positive Δk, and hence, a lower steady‐state toughness. This behavior is enhanced when microcracks link with the main crack to promote further extension.

Fracture characteristics of sisal fibre reinforced concrete

This work is aimed at establishing the fracture characteristics of sisal fibre reinforced concrete, using a model similar to the one proposed by Visalvanich and Naaman for the fracture characterization of steel fibre reinforced concrete. A theoretical fracture model equation, requiring as imput experimental data obtained from tests on notched tensile specimens, is developed to predict the crack resistance curve for sisal fibre concrete. This model can predict the steady state fracture energy G c, using as input parameters the volume fraction of the fibre V f, the length of the fibre L f and the fibre diameter φ. In order to confirm the validity of the theoretical model, experimental data for computation of fracture energy was obtained from several fracture tests using double cantilever beam specimens. Close correlation is seen between the fracture energy curve as obtained from test measurements and the proposed theoretical model. It is also shown that the concept of critical crack opening angle (CCOA) as a fracture criterion is applicable to sisal fibre reinforced concrete, and is found to be a function of the fibre reinforcing parameter, V fL f/φ.

Influence of loading rate on the crack resistance curve and the initiation temperature

This investigation is concerned with the influence of temperature and loading rate on elastic-plastic fracture in the range of ductile cleavage transition. Side-grooved three point bend specimens of a width of 200 mm and a thickness of 100 mm of two steels of the type 22 NiCrMo 37 of different toughness have been loaded with two deflection rates differing by a factor of 10 5 in the range between initiation and upper shelf temperature. Due to dynamical loading the transition temperature of these steels has been increased by about 30 K. The slope of the crack resistance curve of the steel of lower toughness was increased considerable due to dynamical loading whereas the slope of the crack resistance curve of the steel of high toughness was increased only negligible. The results suggest that a conservative assessment of dynamically loaded components may be based on quasi-static crack resistance curves. However, in the case of dynamical loading stable crack growth can be supposed only at temperatures being considerable higher than for quasi-static loading.

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 (JR-) curve. Only above 300°C, the JR-curves obtained from constant-load tests start to deviate substantially from constant-displacement-rate tests. In this temperature range, the Ct-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.

Crack resistance curves of alumina at high temperatures

Ceramic three-point bend specimens were pre-cracked in a displacement-controlled test in air at room temperature to form sharp cracks of different lengths. Critical stress intensity factors (Klc) were then measured as a function of sharp crack length in a fast-fracture, load-controlled test at 900, 1000 and 1100° C. By means of these fast fracture tests, crack resistance curves (Klc against crack length) were determined for two commercially pure aluminas of different grain size and for a debased alumina containing a glassy phase. The crack resistance curve for the pure, fine grained alumina proved to be flat at 900° C, as was found for room temperature. A steeply rising crack resistance was, however, observed for the pure coarse-grained alumina at 1100° C and for the debased alumina at 1000 and 1100° C. This rise in KR curves is explained by friction effects of the cracked microstructure behind the crack front for the coarse grained alumina and by adhesive forces caused by the second phase behind the crack front for the debased alumina. These facts are proved by comparison to experiments on notched specimen and by annealing experiments. From the annealing experiments the size of the adhesive zone is estimated for the debased material.

The influence of loading rate on fracture resistance of notched and precracked ISO-V-specimens

Higher loading rates are expected to have a disadvantageous influence on fracture parameters. This opinion derives probably from experience with ductile-cleavage transition whose temperature increases with increasing loading rate. As far as results on the influence of loading rate on crack resistance are published in the literature they show mostly increasing initiation values as well as increasing crack resistance with increasing loading rate. The paper deals with the influence of loading rate on fracture resistance of notched and precracked ISO-V-specimens measured on different materials. The crack resistance of notched specimens has been determined in analogy to that one of the precracked specimens. The influence of loading rate was separately investigated with regard to initiation as well as to tearing modulus. The results demonstrate that the ratio of dynamic to quasi-static values decreases with increasing toughness, the initiation values for dynamic loading may drop at high toughness below those for quasi-static loading, the slope of the crack resistance curve for dynamic loading is mostly larger than for quasi-static loading and the ISO-V-specimens fall well into line with the results of valid tests.

Yielding- and fracture behaviour of ferritic steels in the transition region of quasistatic to dynamic loading

This paper presents results of investigations on the influence of loading rate on yielding and fracture behaviour of ferritic steels. The range of loading rates was below a certain level at which a special stress wave analysis is required. Concerning the yielding behaviour it was found, that the yield strength can be predicted by the model of thermally activated flow. The strain hardening dσ/dε appeared to be independent of strain rate, if adiabetic heating can be neglected. Concerning the fracture behaviour it is demonstrated that the K lc- T-curves are shifted to higher temperatures with increasing loading rate. The temperature shift could be correlated with the strain rate sensitivity m = d lnσ/d lnε. The ductile/brittle transition temperature increases with incrasing loading rate. For the upper shelf region crack resistance curves as a function of loading rate are presented. It is shown that the crack length can be determined using the key-curve-method. A slightly increasing tendency of the evaluated J R-curves was found.

Crack resistance curves of alumina and zirconia at room temperature

Ceramic three-point bend specimens were pre-cracked in a displacement-controlled test in air at room temperature to form sharp cracks of different lengths. Critical stress intensity factors (K IC were then measured as a function of sharp crack length in a fast-fracture, load-controlled test. Crack resistance curves (K IC against crack length) were determined for three commercially pure aluminas of different grain size, a debased alumina containing a glassy phase, and a partially stabilized zirconia (PSZ) material. The crack resistance curves proved to be flat for the finer-grained and the debased alumina. A steeply rising crack resistance curve was, however, observed for a pure coarse-grained alumina material which is explained by friction effects of the cracked microstructure behind the measured crack front. The effect is influenced by the test procedure itself. Though crack branching takes place the crack resistance curve of PSZ is completely flat, which is attributed to fast fracture testing where only the most dangerous flaw is activated.

Charpy upper shelf energy and crack resistance

Abstract The correlation between Charpy upper shelf energy and crack resistance was investigated by means of instrumented impact tests (ISO-V specimens) and fracture mechanics tests (CT specimens) using four different steels. The strict definition of the Rice J-integral was not applied to the ISO-V specimens. Defining J as the first derivative of deformation energy, it was possible to obtain crack resistance curves of ISO-V specimens and CT specimens. This correlation has been obtained in steels of yield strength between 365 and 480 N/mm2 and is independent of the material. The mechanical basis of this relation can be understood in terms of the criterion for ductile fracture. 60 to 80% of the upper shelf energy is consumed by stable crack growth according to these experiments. The upper shelf energy is useful as a screening test for crack resistance curves. More definite crack resistance values can be estimated from instrumented impact test carried out in dependence on temperature. It seems to be possible to estimate the required upper shelf energy to be specified in regulations with respect to ductile failure safety on the basis of materials mechanics.

Cyclic corrosion crack resistance curves of certain vessel steels

ant layer, damage may occur in the facing [4] and, consequently, contact of the working medium with the vessel pearlitic steel is possible. This in combination with the very severe service conditions of water-cooled-water-moderated power reactors (low loading frequency, high cycle stress ratio, increased temperature, etc.) accelerates corrosion fatigue failure. Statistically [5] it has been established that 30-40% of all damage to power unit high-pressure vessels is related to the formation of corrosion mechanical cracks, pits, pitting, and other defects. Growth of such defects is significantly intensified under the combined action of force loads and the liquid medium, which may lead to failure of the reactor veseel. Therefore, in the design stage of a water-cooled-water-moderated power reactor it is very important to determine the probability of occurrence of such a danger during its design operating life. For this purpose and also for designation of the preventive maintenance schedule of the reactor, data on the rules of corrosion fatigue crack development in vessel steels taking into consideration the actual service conditions is necessary. The primary material for production of reactor vessels is 15Kh2MFA (water-cooled-watermoderated power reactors up to 440 MW) and 15Kh2NMFA (1000-MW water-cooled-water-moderated power reactors) steels [6-9]. At present their cyclic crack resistance in air has been most studied [10-22], while there is practically no information on crack resistance in the working medium. In connection with this a program of cyclic corrosion crack resistance tests was developed and carried out using a new method [23].

Single Specimen Fracture Toughness Testing of Low Strength Steel Plate Using The Direct Current Electrical Potential Method

Abstract The direct current electrical potential method for monitoring of crack length during fracture toughness JIc testing of low strength steels using the crack resistance curve approach is described. The experimental precautions and data processing procedure required for its application are described and discussed. Experimental data obtained from side-grooved, Charpy geometry specimens manufactured from a boiler plate steel are presented.

Slow crack growth in cellulose fibre cements

Slow stable crack growth is a prominent feature of the fracture behaviour of cellulose fibre cements. It is shown that this characteristic can be described by crack growth resistance against crack extension curves based on linear elastic fracture mechanics. Double-cantilever-beam specimens with side grooves are used to obtain such crack resistance curves for a commercial cellulose cement containing approximately 8% mass fraction of bleached fibres. Both dry and wet samples are tested. Compliances measured during slow crack growth by the unloading/reloading technique at successive crack increments are less than those obtained for saw-cut notches with similar crack lengths. Residual displacements due to either mismatch fracture surfaces or a large inelastic process zone at the crack tip are also observed at zero load. A modified elastic potential energy release rate (G R * ), and hence its equivalentK R * [= (EG R * )1/2], must be used to include this residual displacement effect in order to yield the true crack growth resistance curves. This is found to be necessary for the wet samples due to their large residual displacements. The crack growth resistances of the wet samples are superior to those of the dry samples: this is explained in terms of the improved ductility and toughness of the wet cellulose fibres.

Time dependence of J-integral

Tests performed within the framework of earlier RWTÜV projects together with results obtained elsewhere with regard to the time dependence of fracture mechanics data show that time effects reduced the toughness of materials, according to the nature of the test (extremely slow load rate or hold times with sustained load). Reduction in toughness has an effect on the following: • - decrease in critical material data ( J 0, δ i) • - levelling off of the crack resistance curve J = J( Δa) and in consequence a decrease of tearing modulus. This tendency is confirmed quantitatively by recent test results. These tests were performed with the material 15 Mn Ni 63 at room temperature with hold times under sustained load and according to the appropriate standards (without hold times). The tests show that hold times cause additional stable crack growth. The resulting J − Δa curve is lower and less sloping than the curve obtained in a standardized test. The time effect should be taken into account in a safety analysis.

Crack Resistance Behavior of Ceramic Materials

Notched three‐point bend specimens of two aluminas were precracked to form long sharp cracks of varied lengths in a displacement‐controlled experiment at room temperature. Critical stress intensity factors were then measured in a load‐controlled test at high loading rates as a function of sharp crack length. The crack resistance curves (KIc vs crack length) proved to be independent of crack length.

Finite Element Analysis Of The Slow Crack GrowthProcess

A nonlinear finite element analysis, based on the incremental theory of plasticity with isotropic hardening rule, has been performed for the process of slow crack growth in center-cracked specimens made of 2024-T3 aluminum alloy. With experimental data relating the applied stress and the crack size taken as input, it is found that the plastic energy and the crack size are linearly related during the entire process of slow crack growth. Moreover, the linear relation between the plastic energy and the crack size, replacing the experimental applied stress vs. crack size curve, may also be taken as the input and generate a crack resistance curve which is in excellent agreement with the experimental result. This finding enables one to establish a fracture law which can be used to identify the onset of slow crack growth and the onset of fast fracture. Also, a non-self-similar crack growth process has been analyzed for a cracked specimen subjected to monotonically increasing biaxial and shear loading until the point of fast fracture is reached. The orientation and the amount of crack growth are determined by the equivalent maximum opening stress criterion and the linear relation between the plastic energy and the crack size, respectively.

Fracture Behaviour of Binary Styrene/Butadiene Block Copolymer Blends

Morphology and fracture behavior of binary block copolymer blends (triblock and star block copolymers being made up of styrene and butadiene) have been studied via transmission electron microscopy (TEM) and instrumented Charpy impact testing. The toughness of the ductile blends has been characterized by dynamic crack resistance curves (R-curves). The lamellar star block copolymer shows nearly elastic behavior of small scale yielding and unstable crack growth. Addition of 20 wt % of a triblock copolymer comprising polystyrene domains dispersed in rubbery matrix leads to a strong increase in toughness. The mechanism of toughness modification, based on the nanophase-separated structures, represents a specific morphology-toughness correlation which differs fundamentally from toughening mechanisms observed in conventional polymer blends.DOI: 10.3126/jncs.v22i0.523Journal of Nepal Chemical Society Vol. 22, 2007, pp. 55-66