J-integral Values Research Articles

An Evaluation of Fracture Toughness of Graphites for High Temperature Gas-Cooled Reactors by the ISRM Core Testing Method used jointly with AE Method

The fracture toughness test together with the acoustic emission method (AE) was conducted on a fine-grained isotropic graphite (IG-11) and a coarse-grained near isotropic graphite (PGX) for the core components of High Temperature Gas-Cooled Reactors. Three different kinds of specimens were used: a cylindrical three point bending, a short rod and a round compact tension specimens.These cylindrical specimens were proposed as the standard fracture toughness test method at the International Society for Rock Mechanics (ISRM).We have used the J-integral as a parameter of the fracture mechanics, taking into consideration non-linearity of deformation observed in the graphites used here. The J-integral value (JiAE) which was evaluated by AE method was constant independent of specimen shapes. On the basis of the results, the fracture toughness values KIC of the graphites were evaluated: 1.04 MPa√m for IG-11 and 0.77 MPa√m for PGX . In addition, the effect of specimen size on the JiAE values was examined.

Thickness Effect on Elastic-Plastic Fracture Toughness

This paper examines the effect of plate thickness on ductile fracture toughness. Both numerical and experimental investigations are discussed. Considerable attention is paid to the stress, strain and deformation in the vicinity of the crack tipin order to analyze fracture behavior. Fracture toughness tests are performed for center-cracked specimens of SUS430 stainless steel and compact tension specimens of SS41 mild steel. A method to evaluate the critical J-integral value at the onset of crack extension is also proposed.

Critical J-Integral Value of Injection-Molded Polycarbonate Using a Low Thermal Inertia Mold

Abstract A low thermal inertia mold (LTIM) is evaluated based on its ability to reduce residual stress and molecular orientation in thin polycarbonate parts. The mold employs a special cavity design which incorporates the use of high-temperature (above 350 °C) thermoelectric devices. Residual stresses are compared in LTIM and conventionally molded parts via an estimation of critical J-integral values (Jc)-the essential energy needed for crack initiation per unit area. The estimated values of Jc for LTIM and conventional parts are 6.3 and 7.3 kJ/m2, respectively. This difference may be due to the elevated LTIM cavity temperature which alleviates residual stresses and in turn reduces the estimated value of Jc. Observations of birefringence distributions were used to compare molecular orientation. The amount of birefringence is greatly reduced in a large central region of the LTIM parts, indicating low levels of orientation. Conventional parts show distinct color fringes along the melt flow path, indicative ...

Composite Grating For Moire Interferometry

This paper presents the theoretical background and experimental verification of a new composite grating with two different grating frequencies, which was developed for simultaneous measurements of small and large displacements in a single specimen using moire interferometry. A composite grating with line frequencies of 1200 and 300 lines/mm was used to study the changes in the displacement field and the approximate J-integral values of a 5152-H32 aluminum, single-edge-notched specimen under increasing load.

Fully plastic solutions for surace-cracked plates subjected to bending loads.

Finite element analyses are performed on the assumption of the power-law hardening and the deformation theory of plasticity. The J-integral values under the fully plastic condition are estimated for four semi-elliptical or semi-circular surface cracks in plates subiected to bending loads. Some discussions are made concerning the J-integral distributiom along the crack front. The maximun J -integral value is found near the free surface for deep cracks. Also the numerical solutions are applied to the simplified estimation of the growing crack geometry. The crack growth in the width direction is dominant for deeper cracks. As a result, penetration through the plate-thickness does not occur in all cases analyzed.

Fracture characterization of short glass fiber reinforced thermoplastic polyester in mixed mode (I, II) by the J-integral

The crack initiation ( J c) of short glass fiber reinforced thermoplastic polyester (polybutylene terephthalate) under a mixed mode (I, II) loading condition was characterized by the J-integral. Tensile tests were performed with center cracked specimens having angle β between the crack plane and the direction of loading. J c values for different values of β were obtained from the slopes of least square fitted lines relating the strain energy to initial crack length. The strain energy was obtained by subtracting the remotely dissipated energy from the total energy. J I and J II values are estimated from the experimentally obtained J-integral value of a mixed mode crack. Based on such an estimation, it is shown that the J c of a mixed mode crack can be evaluated from J Ic , J IIc and β.

On the determination of fracture toughness in polymers

A method for finding the critical J-integral value, J c, utilizing the locus line of crack initiation points, is found to be useful in determining the fracture toughness of polystyrene (PS), modified polymethylmethacrylate (PMMA), and polypropylene (PP) homopolymer. This method is also shown to be useful in determining the fracture energy at other critical points, such as the maximum load points which can occur in the nonlinear region of the load and load-point displacement curves. A theoretical equation for the calibration factor Φ for linear elastic materials is utilized in determining J c values of polycarbonate (PC), nylon, and vinyl ester from a single test specimen. The critical J-integral values calculated using Φ or based on the locus line of crack initiation points which occurred in a fairly linear elastic range are compared with the values obtained using the critical stress intensity factor K c.

A method to determine the critical J-integral value independent of initial crack sizes and specimen lengths

A method to determine the critical J-integral value independent of initial crack sizes and specimen lengths

Crack-Tip-Acuity Effect on Crack Growth Initiation

For a stationary crack of an initially finite root radius in plane-strain tension, the strain fields around the smoothly blunted crack-tip are calculated for each deformation stage using the slipline field method for nonhardening plastic material. The crack growth initiation from the blunt crack-tip in small-scale yielding, with a full triaxiality ahead of the crack-line, is predicted based on the fracture criterion of the fracture strain at a characteristic distance, obtained by applying the criterion to the case of a sharp crack-tip, in which the effect of the initial root radius on the strain distribution can be neglected. The predicted toughness for mild steel is in reasonable agreement with an experiment. For other materials, the observed J-integral value at fracture initiation, consistent with the present analysis, increases linearly with the initial root radius, but its rate shows a large deviation from the model, which is discussed due to the shear band development. The analysis also predicts that the toughness of a cracked low-ductility material does not increase by making the initial crack-root profile round, and that the reduced triaxiality at the crack-tip brings about a toughness increase.

Estimation scheme for ductile growth of a semi-elliptical surface crack. A simplified prediction of crack aspect ratio.

Finite element analyses are performed on the assumption of the power-law hardening and the deformation theory of plasticity. The J-integral values under the fully plastic condition are estimated for four semi-elliptical. The J-integral values under the fully plastic condition are estimated for four semi-elliptical surface cracks in a plate subjected to uniform tension. Both local and global estimations are employed, varying the manner of the virtual crack extension. Some discussions are made on the J-integral distribution along the crack front. Especially for a deep crack, the maximum J-integral value is found at some location between the deepest point and the free surface. Also, the numerical solutions are applied to the experimental results obtained by the multi-specimen method. The crack aspect rations during ductile growth are predicted well with reasonable fracture resistance.

An approach to nonlinear fracture mechanics using adina

A post-processor for the ADINA program has been developed to calculate J-integral and J-integral values. The post-processor can deal with relatively complex fracture mechanical behaviors with plastic strains, thermal strains, inertia forces and body forces taken into account This paper presents the results of two fracture mechanical analyses of the center-cracked plate. These results indicate that the J-integral can be considered path-independent even in the presence of plastic strains and inertia forces, and that it can hold a constant value during the stable crack growth.

A method to evaluate critical J-integral value: Locus method

A method which evaluates the critical J-integral value (J c) by utilizing the locus of crack initiation points on load-displacement records is presented. This method partitions the fracture energy along the locus line based on an energy rate interpretation. The shape of the locus line depends on both the material and the configuration of the specimen. Since the fracture energy can be partitioned even along a nonlinear locus line, the method is also suitable for highly deformable materials, which usually exhibit a nonlinear locus line. In order to validate this point, a thermoplastic rubber was used for experimental study. The experimental results show that J c can be evaluated by this method without restricting the ratio of the initial crack length to the specimen width (a/w) or the specimen length provided that the locus line can be located on the load-displacement record.

Elastic-plastic calculations of the fracture mechanical behaviour of a precracked pressure vessel with fluid-structure interaction

By means of ADINA extended by fracture mechanical options elastic-plastic calculations were carried out for an experimental burst vessel with a long axial outer notch. With a 2-d model initiation, stable growth and instability of the crack is investigated. At the burst pressure the crack becomes a slit. Then the vessel is loaded by time dependent internal pressure distributions which were evaluated with a fluid code. The dynamic, elastic-plastic behaviour is analyzed with a 3-d model. Concerning fluid-structure interaction, the influence of modifications in the pressure distributions is investigated. Instable crack growth and crack arrest are taken into account. Dynamic J-integral values and leak areas were calculated using additional routines implemented in the ADINA program. Analytical and experimental results are compared.

Fracture Toughness Design In Horse Hoof Keratin

An engineering fracture mechanics approach was applied to the analysis of the fracture resistance of equine hoof-wall. The relationship between fracture toughness and the morphological organization of the keratin hoof tissue was investigated. Fracture toughness was evaluated using the J-integral analysis method which employs the compact tension test geometry. Tensile tests were also conducted to evaluate the effect of the morphological organization on the stress-strain behaviour. Hoof-wall has greatest fracture resistance for cracks running proximally, parallel to the tubular component of the wall keratin. For fully hydrated material tested in this direction the mean critical J-integral value at failure was 1.19 X 10(4)J m-2. This was nearly three times greater than the value determined for the weakest orientation, in which the crack ran parallel to the material between the tubules. The lower fracture toughness of the intertubular material dominates the fracture behaviour of this tissue. The tubular components of the wall appear to reinforce against fracture along the weak plane and the entire wall organization provides the mechanical capability for limiting and controlling fracture in this tissue.

Elasto-plastic stress analysis of a CT specimen using method of lines

The elastic formulation for the Method of Lines is extended to include the small scale plasticity effects. The Von-Mises criterion, isotropic hardening and the Prandtl-Reuss equations are used. A set of coupled nonlinear ordinary differential equations are derived and applied to compact tension specimen. The resulting set of equations are solved iteratively by using a combination of a recurrence relations method and the successive elastic solution method. A load versus crack mouth opening displacement diagram obtained numerically is compared with experimental results. The J-integral values are also calculated for different paths through the specimen at several locations through the thickness. The J values were found to be significantly path dependent for paths near the crack tip at loads well above that producing incipient yielding. It was found that the enhanced version of the Method of Lines yields very good results

Effect of Hydrostatic Pressure on Fracture Toughness : 2nd Report, Elastic-plastic Fracture Toughness

To investigate the effect of hydrostatic pressure on the fracture toughness of boron steel and aluminum alloy, a compact tension test based on ASTM Standard is carried out under pressure up to 400 MPa. The displacement at the crack initiation is detected by an electric potential difference method under pressure. The elastic-plastic fracture toughness JIC increases with an increasing increasing pressure. The phenomenon of the increase of fracture toughness due to pressure is confirmed by measuring a critical stretch zone width of boron steel. The experimental JIC values are compared with the J-integral values analyzed by FEM.

Experimental and analytical estimates of the J-integral for tensile panels containing short center cracks

The finite element method (FEM) is used to predict the applied J-integral values in highly strained tensile panels containing short center cracks. Experimental J-values are obtained by integrating strain and displacement quantities measured along an instrumented contour. FEM plane stress predictions for J-values and crack mouth opening displacements (CMOD) are much larger than experimentally measured values for short cracks (a/W<0.05). Large geometry changes near the crack tip are demonstrated to have a negligible effect on the FEM J and CMOD values. The introduction of a small stiffened zone near the crack tip using an overlay of plane strain elements brings FEM J and CMOD values into close agreement with experimental values. For longer crack lengths, conventional plane stress FEM solutions are adequate to predict J and CMOD values.

A comment on JI-R curve chracterizing stable crack growth.

Stable crack growth experiments for SM 50 A steel and 2017-T3 aluminum were carried out to obtain JI-R curves under crack-line wedge loading and 3-point bending. J-integral value, which was computed by use of the formula for a growing crack recommended by ASTM, increased at different rates with the crack growth amount under both type loadings while the values at initiation equaled. Finite element analysis was made for the stable crack growth measured by the experiment to compute the J-integral value at the growing crack tip. In elasto-plastic materials, elastically unloaded region is left behind the growing crack tip. This region lets J-integral lose the path independency. J-integral value at growing crack tip was computed from the integration of J along the specimen outer contour and correction for the unloaded region. The computation results showed that the J-integral value at the crack tip was almost invariable while the crack grew and was independent of the loading type.

A study about Ji, and δi, in three-point bend specimens with deep and shallow notches

An experimental study for determining δ i , and J i , in three-point bend specimens with both shallow and deep notches has been described. A new method for obtaining δ i is simply introduced. Two clip gauges were used, P- V and P- Δ plots were simultaneously obtained on the same specimen. COD values were obtained from both P- V and P- Δ plots. Experimental results of three different heat-treated alloy steels show that the crack opening displacement and J-integral values of shallow cracks at initiation are much larger than those of deep cracks. The relationship of COD and J-integral is also studied.

J-integral analyses of plate and shell structures with through-wall cracks using thick shell elements

A new evaluation method using thick shell elements is proposed to calculate the distribution of the J-integral values along crack fronts of through-wall cracks in plate and shell structures. Dividing tentatively the thick shell elements into several layers in the thickness direction, integral paths are defined at each layer to obtain the thickness distributions of the J-integral values of through-wall cracks in plate and shell structures. The three-dimensional definition of the J-integral is used to calculate the J-integral value at each layer. The results of several stress intensity factor analyses are presented to show the effectiveness of the present evaluation method. The distribution of the J-integral value along a crack front is also compared between the methods using the thick shell elements and the three-dimensional solid elements.