THE ANALYSES OF THE THREE-DIMENSIONAL STRESS STRUCTURE NEAR THE CRACK TIP OF MODE I CT SPECIMENS IN ELASTICPLASTIC STATE(Ⅰ)—THE ANALYSES OF CONSTRAINT PARAMETERS AND FRACTURE PARAMETERS

In the present paper, three dimensional analyses of some general constraint parameters and fracture parameters near the crack tip. of Mode I CT specimens in two different thicknesses are carried out by employing ADINA program. The results reveal that the constraints along the thickness direction are obviously separated into two parts: the keeping similar high constraint field (Z₁) and rapid reducing constraints one (Z₂). The two fields are experimentally confiremed to correspond to the smooth region and the shear lip on the fracture face respectively. So the three dimensional stress structure of Mode I specimens can be derived through discussing the two fields respectively. The distribution of the Crack Tip Opening Displacement (CTOD) along the thickness direction and the three dimensional distribution of the void growth ratio (V_g) near the crack tip are also obtained. The two fracture parameters are in similar trends along the thickness direction, and both of them can reflect the effect of thickness and that of the loading level to a certain degree.     

Mixed Mode Dynamic Fracture in Particulate Reinforced Functionally Graded Materials

A detailed analytical and experimental investigation is presented to understand the dynamic fracture behavior of functionally graded materials (FGMs) under mode I and mixed mode loading conditions. Crack-tip stress, strain and displacement fields for a mixed mode crack propagating at an angle from the direction of property gradation were obtained through an asymptotic analysis coupled with a displacement potential approach. This was followed by a comprehensive series of experiments to gain further insight into the behavior of propagating cracks in FGMs. Dynamic photoelasticity coupled with high-speed photography was used to obtain crack tip velocities and dynamic stress fields around the propagating cracks. Birefringent coatings were used to conduct the photoelastic study due to the opaqueness of the FGMs. Dynamic fracture experiments were performed using different specimen geometries to develop a dynamic constitutive fracture relationship between the mode I dynamic stress intensity factor (K _ID ) and crack-tip velocity ( ) for FGMs with the crack moving in the direction of increasing fracture toughness. A similar -K _ID relation was also obtained for matrix material (polyester) for comparison purposes. The results obtained show that crack propagation velocities in FGMs were about 80% higher than the polyester matrix. Crack arrest toughness was found to be about 10% lower than the value of local fracture toughness in FGMs.     

R-similarity criterion of plastic deformation instability and its use for KIC determination for steels

The paper reports an investigation of the application of the similarity theory, strain energy density concept and fracture mechanics to the fracture toughness (K_IC) determination. The method K_IC determination is described using R-similarity criterion of plastic deformation instability. It allows to determine the true K_IC value for ductile steels using specimens not satisfying linear fracture mechanics requirements.     

An indentation technique for estimating the energy density as fracture toughness with Berkovich indenter for ductile bulk materials

A technique is proposed to estimate the energy density as fracture toughness for ductile bulk materials with an indentation system equipped with a Berkovich indenter based on the theory of plastic deformation energy transforming into the indentation energy of fracture. With progressive increase of penetration loads, the material damage is exhibited on the effective elastic modulus. A quadratic polynomial relationship between the plastic penetration depth and penetration load, and an approximate linear relationship between logarithmic plastic penetration depth and logarithmic effective elastic modulus are exhibited by indentation investigation with Berkovich indenter. The parameter of damage variable is proposed to determine the critical effective elastic modulus at the fracture point. And the strain energy density factor is calculated according to the equations of penetration load, plastic penetration depth and effective elastic modulus. The fracture toughness of aluminum alloy and stainless steel are evaluated by both indentation tests and K_IC fracture toughness tests. The predicted S_cr values of indentation tests are in good agreement with experimental results of CT tests.     

A method for measuring mode I crack tip constraint under static and dynamic loading conditions

A novel experimental technique for measuring crack tipT-stress, and hence in-plane crack tip constraint, in elastic materials has been developed. The method exploits optimal positioning of stacked strain gage rosette near a mode I crack tip such that the influence of dominant singular strains is negated in order to determineT-stress accurately. The method is demonstrated for quasi-static and low-velocity impact loading conditions and two values of crack length to plate width ratios (a/W). By coupling this new method with the Dally-Sanford single strain gage method for measuring the mode I stress intensity factorK _I , the crack tip biaxiality parameter is also measured experimentally. Complementary small strain, static and dynamic finite element simulations are carried out under plane stress conditions. Time histories ofK _I andT-stress are computed by regression analysis of the displacement and stress fields, respectively. The experimental results are in good agreement with those obtained from numerical simulations. Preliminary data for critical values ofK _I and β for dynamic experiments involving epoxy specimens are reported. Dynamic crack initiation toughness shows an increasing trend as β becomes more negative at higher impact velocities.     

Effect of T-stress on crack growth under mixed mode I–III loading

For a crack subjected to combined mode I and III loading the influence of a T-stress is analyzed, with focus on crack growth. The solid is a ductile metal modelled as elastic–plastic, and the fracture process is represented in terms of a cohesive zone model. The analyzes are carried out for conditions of small scale yielding, with the elastic solution applied as boundary conditions on the outer edge of the region analyzed. For several combinations of the stress intensity factors K_I and K_III and the T-stress crack growth resistance curves are calculated numerically in order to determine the fracture toughness. In all situations it is found that a negative T-stress adds to the fracture toughness, whereas a positive T-stress has rather little effect. For given values of K_I and T the minimum fracture toughness corresponds to K_III = 0.     

Crack growth in glass matrix composite reinforced by long SiC fibres

Theoretical and experimental work are made for bridged cracks in chevron-notched three point bend specimens made of glass matrix composite reinforced by long SiC fibres. The fracture toughness (K_IC) values are determined using the chevron-notch technique and compared with the theoretical predictions based on micromechanical analysis exploiting weight functions. The weight functions for orthotropic material are obtained numerically by means of detailed FEM analysis using the ANSYS package and they are further used together with appropriate bridging models for the theoretical prediction of the R-curve behaviours typical of the investigated composites.     

On determination of mode II fracture toughness using semi-circular bend specimen

The cracked semi-circular specimen subjected to three-point bending has been recognized as an appropriate test specimen for conducting mode I, mode II and mixed mode I/II fracture tests in brittle materials. The manufacturing and pre-cracking of the specimen are simple. No complicated loading fixture is also required for a fracture test. However, almost all of the theoretical criteria available for mixed mode brittle fracture fail to predict the experimentally determined mode II fracture toughness obtained from the semi-circular bend (SCB) specimen. In this paper, a modified maximum tangential stress criterion is used for calculating mode II fracture toughness K_IIc in terms of mode I fracture toughness K_Ic. The modified criterion is used for predicting the reported values of mode II fracture toughness for two brittle materials: a rock material (Johnstone) and a brittle polymer (PMMA). It is shown that the modified criterion provides very good predictions for experimental results.     

An improved experimental method for the determination of the critical stress intensity factor KIc of brittle materials

The critical stress intensity factor K_Ic is determined by a simple and accurate method, using small test specimens and a simple procedure in this paper.Single edge V-notched tension specimens made of PMMA are subjected to a load which is slowly increased until the crack begins to move from the notch tip. During the crack propagation event shadow patterns at the tip of the crack are recorded in a video recorder. Under these loading conditions, the creating real crack propagate slowly until the crack propagation velocity take an abrupt increase and the entire fracture of the specimen takes place. The stress intensity factor which correspond to the transition from the slow to fast crack speed, is the critical stress intensity factor K_Ic and it can be the fracture toughness of the material.The results are accurate and in good agreement with those values of K_Ic which are calculated by approximate theoretical expressions.The purpose of this paper is to introduce an improved, simple and accurate experimental method for the determination of fracture toughness of brittle materials.     

Critique on fracture criteria in mixed-mode-loading

The paper presents an improved formulation of mixed-mode fracture criteria. Both the fracture toughness K_IC and K_IIC are taken into account. Consequently, the crack propagation direction and the fracture envelope in the and plane depends on the toughness ratio . In the plane only one envelope for each criterion is obtained.     

Stress intensity factor and crack velocity relationship for polyester/TiO2 nanocomposites

The dynamic fracture behavior of polyester/TiO₂ nanocomposites has been characterized and compared with that of the matrix material. A relationship between the dynamic stress intensity factor,K _I and the crack tip velocity,å, has been established. Dynamic photoelasticity coupled with high-speed photography has been used to obtain crack tip velocities and dynamic stress fields around the propagating cracks. Birefringent coatings were used to conduct the photoelastic study due to the opaqueness of the nanocomposites. Single-edge notch tension and modified compact tension specimens were used to obtain a broad range of crack velocities. Fractographic analysis was conducted to understand the fracture process. The results showed that crack arrest toughness in nanocomposites was 60% greater than in the matrix material. Crack propagation velocities prior to branching in nanocomposites were found to be 50% greater than those in polyester.     

An Experimental Study of Mixed Mode Crack Initiation and Growth in Functionally Graded Materials

Quasi-static mixed mode crack initiation and growth in functionally graded materials (FGMs) was studied through fracture experiments on polymer-based FGMs manufactured by selective ultraviolet irradiation poly(ethylene carbon monoxide)—a photo-sensitive copolymer that becomes more brittle and stiffer under ultraviolet irradiation. The objective of the study was to determine whether crack kinking criteria for homogeneous materials, e.g., maximum hoop stress criterion, also hold for FGMs. Single edge notched tension specimens with different spatial variations of Young's modulus, failure stress and failure strain, were tested. Near tip mode mixity was introduced either by inclining the crack to the remote loading direction, as in the case of homogeneous materials, or to the direction of material gradient, or both. A full-field digital image correlation technique was used to measure in real-time the displacement field around the crack tip while it propagated through the graded material, and to extract the fracture parameters of stress intensity factor K _I and K _II , and the T-stress. It was found that the nonsingular T-stress term in the asymptotic expansion for stresses plays a very important role in accurately measuring fracture parameters. It was also found that the maximum tangential stress criterion can be applied to the case of FGMs to predict crack kinking provided that the effect of the T-stress is accounted for and the process zone size is small compared to the intrinsic material gradient length scale. However, for accurate crack path prediction at a length scale comparable to the material gradient, detailed material property information is required. In general, the crack will propagate towards a region that exhibits less fracture toughness, but, unlike the case of homogeneous materials, along a path where K _II is not necessarily equal to zero.     

A study ofJ-integral of the orthotropic composite material

The relation between J-integral near model I crack tip in the orthotropic plate and displacement derivative is derived in this paper. Meanwhile, the relation between stress intensity factor K _I and displacement is also given in this paper. With sticking film moire interferometry method, the three-point bending beam is tested, thus the values of J-integral and K _I can be obtained from the displacement field, and then the truth of relation formula between J-integral and K _I in the orthotropic composite materials is experimentally verified.     

An experimental—Numerical evaluation of the<Emphasis Type="Italic">T</Emphasis><Stack><Subscript>ε</Subscript><Superscript>*</Superscript></Stack> integral for a three-dimensional crack front

TheT _ε ^* integral was calculated on the surface of single edge notched, three-point bend (SE(B)) specimens using experimentally obtained displacements. Comparison was made withT _ε ^* calculated with the measured surface displacements andT _ε ^* calculated at several points through the thickness of a finite element (FE) model of the SE(B) specimen. Good comparison was found between the surfaceT _ε ^* calculated from displacements extracted from the FE model and the surfaceT _ε ^* calculated from experimentally obtained displacements. The computedT _ε ^* integral was also observed to decrease as the crack front was traversed from the surface to the mid-plane of the specimen. Mid-planeT _ε ^* values tend to be approximately 10% of the surface values.     

Effect of transverse stress on switch-toughening of ferroelectrics

Testing data indicated that T stress significantly altersR-curves of ferroelectrics. The model of stress-induced polarization switching is adopted to evaluate the fracture toughness of ferroelectrics under K field and T stress. Analytical solution is obtained to estimate the steady state fracture resistance of mono-domain ferroelectrics. The result is generalized to multi-domain ferroelectric ceramics via Reuss approximation, which enables us to explain quantitatively R-curves under two testing configurations.     

A novel method for measuring and characterizing dynamic fracture-initiation toughness of elastic-plastic materials

The characterization and testing methods of the dynamic fracture initiation toughness of elastic-plastic materials under tensile impact are studied. By using the self-designed bar-bar tensile impact apparatus, a novel test method for studying dynamic fracture-initiation has been proposed based on the one-dimensional test principle. The curve of average loadv. s. displacement is smooth until unstable crack propagation, and the kinetic energy which does not contribute to the crack growth can be removed from total work done by external-force to the specimen. The fracture-initiation point is determined by compliance-changing rate method. The results show that these methods are feasible and effective. Through the analysis of the conversion between work and energy of a fracture specimen, the dynamicJ-integral is adopted as a characteristic parameter for elastic-plastic materials under impact loading. TheJ-integral is calculated from and curves by using the formula proposed, by Rice. TheJ-integral at fracture initiation is employed to describe the dynamic fracture-initiation toughness of elastic-plastic materials and the experimental results indicate thatJ _ID can be regarded as a material constant.     

Brittle fracture: Variation of fracture toughness with constraint and crack curving under mode I conditions

The effect of constraint on brittle fracture of solids under predominantly elastic deformation and mode I loading conditions is studied. Using different cracked specimen geometry, the variation of constraint is achieved in this work. Fracture tests of polymethyl methacrylate were performed using single edge notch, compact tension and double cantilever beam specimens to cover a bread range of constraint. The test data demonstrate that the apparent fracture toughness of the material varies with the specimen geometry or the constraint level. Theory is developed using the critical stress (strain) as the fracture criterion to show that this variation can be interpreted using the critical stress intensity factorK _Cand a second parameterT orA ₃,whereT andA ₃are the amplitudes of the second and the third term in the Williams series solution, respectively. The implication of this constraint effect to the ASTM fracture toughness value, crack tip opening displacement fracture criterion and energy release rateG _Cis discussed. Using the same critical stress (strain) as the fracture criterion, the theory further predicts crack curving or instability under mode I loading conditions. Experimental data are presented and compared with the theory.     

Initiation and arrest of cracks on two pipeline steels at low temperature

Dynamic fracture toughness at initiationK _1d and fracture toughness at arrestK _1a were measured on two pipeline steel grades. Dynamic fracture toughness was measured at a very high loading rate with the help of split Hopkinson pressure bars. The values ofK _1d andK _1a are compared. The purpose of this work is to examine the possibilities of using dynamic fracture toughness at crack initiation as a lower bound of crack arrest toughness. This work has practical applications because crack arrest tests are difficult to perform, give scattered results and are costly and time consuming. This procedure shows that it is possible to economize and rationalize using intelligent technology.     

On the use of crack-tip-opening displacement to predict the fracture strength of notched graphite/epoxy laminates

The fracture strength and crack-opening displacement of notched graphite/epoxy laminates were measured experimentally using the center-cracked tension-specimen geometry. Four replicate tests were conducted for a variety of laminate stacking sequences, thicknesses, and notch lengths. Most laminates exhibited extensive notch-tip damage prior to fracture. Values of crack-tip-opening displacement (CTOD) at fracture were estimated from values of crack-opening displacement measured at the crack center line. CTOD was independent of specimen crack length for the [0/±45/90] _s , [0/±45/90]_15s , [0/±45] _s , [0/±45/]_15s , and [0/90]_24s laminates. In addition, notched laminate strength was accurately predicted using a Dugdale-type model along with the estimated CTOD.Paper was presented at V International Congress on Experimental Mechanics held in Montreal, Quebec, Canada on June 10–15, 1984.     

Degradation of nylon-6/clay nanocomposites in NO<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>

Nylon-6 is an important engineering polymer that, in its fully spherulitic (bulk) form, has many applications in gears, rollers, and other long life cycle components. In 1993, Toyota commercialized a nylon-6/clay nanocomposite out of which it produced the timing belt cover for the Camry. Although these hybrid nanocomposites show significant improvements in their mechanical response characteristics, including yield strength and heat distortion temperature, little is known about the degradation of these properties due to environmental pollutants like NO _x . Nylon-6 fibers are severely degraded by interaction with NO _x and other pollutants, showing a strong synergy between applied load and environmental degradation. While the nanocomposites show a significant reduction in permeability of gases and water due to the incorporation of lamellar clay, their susceptibility to nondiffusional mechano-chemical degradation is unknown. The fracture toughness of these nylon-6/clay nanocomposites increases, not as a function of clay content, but as a function of the volume of nylon-6 polymer chains influenced by the clay lamellae surfaces. Both the clay and the constrained volume offer the nanocomposites some protection from the deleterious effects of NO _x . The time-to-failure at a given stress intensity factor as a function of clay content and constrained volume is discussed along with fracture toughness of the materials.