Critical Fracture Stress Research Articles

Influence of finite width on notched laminate strength predictions

Notched strength of composite laminates is commonly predicted by first determining the stress distribution within the laminate and subsequent application of a stress fracture criterion. Common test specimen geometries typically require finite width stress distributions for correct data reduction and strength predictions. Numerical difficulties are encountered with this approach, however, because closed-form expressions for the stress distribution in orthotropic materials exist only for infinite width-to-hole diameter (w/D) geometries. In this paper, finite element stress analysis is presented for isotropic and orthotropic plates containing circular notches. Results are correlated with available analytical solutions. For geometries where w/D < 4 there is a substantial change in the normal stress distribution and related strength predictions. An approximate finite width stress distribution for orthotropic plates with circular notches is proposed and the influence of finite width on notched strength predictions is discussed.

Numerical prediction of the fracture of a thick pressurized shell subjected to a liquid nitrogen shock

The probabilistic elastoplastic stress criterion for cleavage fracture is used in the frame of the local approach to fracture to analyse a fracture experiment in which a one meter long cylinder, with a longitudinal straight crack, was submitted to a thermal shock by liquid nitrogen. The computation, which gives the variation of the probability of fracture with time during the cooling transient, leads to predict a value for the most probable fracture time which is very close to the experimental one. The LEFM approach, which would predict a later initiation time can be improved by incorporating the probabilistic criterion in the frame of the small scale yielding analysis.

Dynamical fault rupture processes in heterogeneous media

The fault rupture processes in a horizontally layered medium and also in a three-dimensionally heterogeneous structure are investigated on three-dimensional, spontaneous dynamic shear crack models. The wave equations for three-dimensional space are solved numerically by a finite difference scheme under the appropriate boundary conditions and the finite stress fracture criterion. The heterogeneous properties of the elastic medium, particularly the existence of low-velocity zones, give remarkable effects on the rupture process, yielding appreciably decelerated rupture velocities and large fault displacements in and around the zones and strong motions in the near-field. The large fault displacements are enhanced when the rupture breaks the ground surface. The static seismic moment in the case with a low-velocity zone is essentially the same as in a homogeneous half-space. An attempt is made to simulate the rupture process of a moderate-size earthquake, by applying the above shear crack model in a heterogeneous medium with depth-dependent and laterally heterogeneous stress drop. The model appears to explain the observed features to a satisfactory degree.

Laminated Composites Containing an Elliptical Opening. I. Approximate Stress Analyses and Fracture Models

Approximate stress analyses are presented for orthotropic composite laminates contain ing an elliptical opening under uniaxial normal loads. Examining by the use of exact elasti city solution shows that these approximate solutions have excellent accuracy. Utilizing these solutions, the point stress fracture criterion and the average stress fracture criterion are generalized for the strength prediction of fiber-reinforced composite laminates contain ing an elliptical opening. Comparisons show that these models have good correlation with experimental data.

Laminated Composites Containing an Elliptical Opening. II. Experiment and Model Modification

Static tensile experiment was performed for orthotropic composite laminates containing an elliptical opening. Based on the extended point stress fracture criterion and the ex tended average stress fracture criterion, a modified model is presented that expresses the characteristic damage zone size as functions of the opening length and opening aspect ratio. The predictions for the notched strength of orthotropic laminates, containing either a circular hole, an elliptical opening, or a center crack, agree very well with experimental data and are written in a tractable form.

Thermal stress fracture of refractory lining components: Part I. Thermoelastic analysis

This paper presents a mathematical model and corresponding stress analysis suitable for the development of theoretical criteria useful for the design and selection of refractory components of linings of high-temperature furnaces and metallurgical process vessels. Refractory lining components, for which the maximum principal tensile stress fracture criterion is assumed valid, are simulated using a two-dimensional constant heating rate thermoelastic model. Dimensional analysis and the finite element numerical method are utilized to develop a general solution for the maximum principal tensile stress in a rectangular shape of arbitrary length and width in terms of thermal and mechanical properties and heating and cooling rate. Implications of the general stress solution with regard to fracture behavior and design recommendations are discussed with reference to results previously reported in the literature.

Thermal stress fracture of refractory lining components: Part II. Safe heating and cooling rates

The solution for the maximum principal tensile stress of a two-dimensional constant heating rate thermoelastic model has been used to develop a resistance-to-fracture-initiation parameter useful for the design and selection of refractory components that accounts for thermal and mechanical properties, geometry, and temperature range, as well as distinguishes between the heating and cooling cases. The parameter, namely safe heating or cooling rate, is defined as the maximum rate at which a rectangular shape can be heated or cooled through a specified temperature range without causing fracture, which is taken to be governed by the maximum principal tensile stress fracture criterion. Computation of the parameter is easily accomplished using a graphical technique. Tabulated values are used to plot dimensionless relationships that give the combinations of variables that both satisfy the fracture criterion and produce a specified value of hot face temperature. Good agreement was found between model predictions of safe heating rate and experimental values reported in the literature.

Thermal stress fracture of refractory lining components: Part III. Analysis of Fracture

The fracture behavior of refractory components heated from one end is simulated using a twodimensional constant heating rate thermoelastic model and the maximum principal tensile stress fracture criterion. Dimensionless graphical relationships that can be used to predict location of fracture and orientation of cracking are presented. Dimensional analysis and the finite element numerical method are used to develop a general solution for the total strain energy. Based on the premise that extent of crack propagation is directly related to available strain energy at fracture and inversely related to the surface energy per unit area, the solution for total strain energy is used to derive a damage resistance parameter useful for the design and selection of refractory components that accounts for material properties, geometry, and heating and cooling rate. Model predictions of location of fracture, orientation of cracking, and extent of crack propagation are in general agreement with experimental results previously reported in the literature. Limitations of the two-dimensional thermoelastic model are discussed.

Interaction of phosphorus, carbon, manganese, and chromium in intergranular embrittlement of iron

AbstractVacuum melted electrolytic iron and alloys of Fe–P, Fe–Mn, Fe–Cr, Fe–Mn–P, and Fe–Cr–P were employed in a study of the effects of chromium and manganese on phosphorus segregation and intergranular embrittlement. The effects of carbon were examined by hydrogen-decarburization of the original low carbon (10–60 ppm) alloys. The critical fracture stress was measured by pure bending of notched bars at 133 K, and the grain boundary compositions were measured by Auger electron spectroscopy. Manganese was found to segregate in the absence of phosphorus and to be a powerful embrittling element. Carbon was found to exert a great intergranular strengthening effect. It also interfered with the segregation of phosphorus; the latter effect was reduced by the presence of chromium, in agreement with the prior report of Erhart and Grabke. In decarburized alloys the presence of manganese caused increased phosphorus segregation but not when carbon was present at 10–30 ppm. Segregation of manganese and chromium were ...

Long-time creep fracture data on 1/2 CrMoV Steel and their application to design

AbstractThe results of 46 tensile creep tests at seven temperature levels are reported along with a single solid torsion test at each temperature over the range 450-600°C, with a longest time to fracture of 132000 h. The torsion tests show the multiaxial stress criterion for creep fracture to be the octahedral shear stress. Analysis of the data leads to a constitutive equation which can be applied to the prediction ofcreep fracture of components using the skeletal point technique. Experimental and predicted behaviour ofsimple biaxial and triaxial components are examined.

The influence of geometry of edge-cracked plates on crack initiation

In this paper the influence of geometry of edge-cracked plates on crack propagate under mixed mode loading conditions is studied. The edge-cracked plates under tension are examined. The crack extension angle and the critical stress of fracture are determined for various values of the crack inclination angle and the ratio of the crack length to specimen's width. The Det.-criterion developed by the author is used.

Mechanical properties of HT-9 as a function of heat treatment

In support of work to assess the failure resistance of HT-9, we have investigated the mechanical properties of specimens heat treated to twenty-five combinations of austenitization temperature, Tγ (950–1200°C), tempering temperature (650–780°C), and tempering time (0.5–56 h). Hardness, strength, and dynamic (lower shelf) fracture toughness were found to be relatively insensitive to Tγ. For a given Tγ the strength was found to decrease and the dynamic (lower shelf) fracture toughness was found to increase slightly with increasing tempering time and temperature. Analyses of the data suggest that the critical cleavage fracture stress σf* decreases with increasing Tγ above 1050°C for a number of tempering conditions, and that σf* decreases with increasing tempering temperature and time for a given Tγ.

Microstructural effects on the cleavage fracture stress of fully pearlitic eutectoid steel

The microstructural parameter(s) controlling the critical cleavage fracture stress, σF, of fully pearlitic eutectoid steel have been investigated. Independent variation of the pearlite interlamellar spacing,Sp, and the prior austenite grain size were accomplished through heat treatment. Critical cleavage fracture stresses were measured on bluntly-notched bend specimens tested over the temperature range -125 °C to 23 °C. The cleavage fracture stress increased with decreasingSp, and was independent of prior austenite grain size. Fine pearlitic microstructures exhibited temperature, strain-rate, and notched-bar geometry independent values for σF, consistent with propagation-controlled cleavage fracture. Coarse pearlitic specimens exhibited temperature-dependent values for σF over a similar temperature range. Inclusion-initiated fractures were generally located at or beyond the location of the peak normal stress in the bend bar, while cracking associated with pearlite colonies was observed to be closer to the notch than the predicted peak stress location. The calculated values for σF were independent of both the type and location of initiation site(e. g., inclusion, pearlite colony). Thus, although inclusions may provide potent fracture initiation sites, their presence or absence does not necessarily change σF in fully pearlitic microstructures.

Flow‐induced chain fracture of isolated linear macromolecules in solution

AbstractThe recently developed elongational flow technique is applied to the examination of flow‐induced chain rupture of macromolecules in solution. For both closely monodisperse atactic polystyrene (a‐PS) and poly(ethylene oxide) (PEO), the critical strain rate for extension (\documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon _c $\end{document}) is found to depend upon molecular weight M as \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon _c \simeq M^{ - 1.5} $\end{document}, consistent with ideal Zimm dynamics. When the chains are subjected to strain rates beyond \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon _f $\end{document} the scission products correspond closely to one‐half of the initial molecular weight. The critical fracture stress depends upon molecular weight as \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon _f \simeq M^{ - 2} $\end{document}, enabling the prediction of the ultimate chain length which can be extended without fracture (\documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon _c = \dot \varepsilon _f $\end{document}). For a‐PS this corresponds to M = 3 × 107. These findings are well accounted for by Stokes' Law applied to an extended bead–rod model. The calculated flow‐induced force in the chain corresponds closely to the rupture force of a covalent backbone bond calculated from a modified Arrhenius rate equation. During the prefracture stage (\documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon _f &gt; \dot \varepsilon &gt; \dot \varepsilon _c $\end{document}) a‐PS shows anomalies in the flow‐induced birefringence, which suggest that the Phenyl side groups are becoming reoriented due to the progressive increase in free volume as the chemical backbone bonds stretch and the bond angles open.

Pressure Effects on Rheological Behavior of Melt Polymers – A Discussion in Relation to Polymer Processing

Abstract Polymers have large bulk compressibility in the molten state /1/ and their rheological properties are largely affected by pressure applied in polymer processing. The volumetric strain induced by pressure consists of instantaneous and retarded elastic strains, both of which are proportional to pressure, and recover reversibly when pressure is removed. In many crystalline polymers, as observed by B. Maxwell for polyethylene, retarded elastic strain is large, and due mostly to pressure crystallization. This paper describes results of experimental studies relating pressure effects on rheological properties of melt polymers with polymer processing and bulk properties of products. The following items are discussed: pressure induced shear stress, analysis of local deformation pattern, critical shear stress for melt flow fracture, relationship between power law index and bulk compressibility, effects of hydrostatic pressure on melt flow behavior, pressure efficiency of injection molding, jetting phenomena, shrinkage in injection moldings, residual strain, and super-high-pressure injection molding process.

Condition of brittle fracture in bending on notched specimens of rigid plastics.

The fracture behavior in bending of notched bars of polycarbonate, polyvinylchloride and polymethyl methacrylate has been investigated. The uniform bending tests of single edge notched plates that are thick enough to yield in plane strain have been carried out for a wide range of notch radii. The experimental results were discussed in terms of the critical maximum stress and the notch root radius. The main results obtained are as follows : (1) The predominant factors for determining the ductile-brittle transition of fracture mode in bending are the notch root radius and thickness of specimen. (2) The critical maximum stress for brittle fracture is governed by notch root radius alone in the case of a constant thickness of specimen. (3) The fracture criterion of notched bar mentioned above, is commonly applied to both tension and bending, and the criterion holds in three kinds of rigid plastics.

The Griffith-Orowan fracture theory revisited: The [formula omitted

In the present paper a new fracture criterion (the T- criterion ) is described. It is based on the Griffith fracture theory, as modified by Orowan, according to which failure is the result of the mutual action of both fracture and yielding mechanisms. The main idea of the T- criterion is that fracture is caused by normal stresses, whose contribution is included in the dilatational part T V of the strain-energy density. It is then postulated that fracture will initiate outside the plastic region surrounding the crack-tip, when T V reaches a critical value. On the other hand, plasticity depends on the distortional part of strain-energy density and its extent is defined by the Mises yield locus, which is used for the calculation of the elastic-plastic boundary, along which T V is computed. Then, the T V = f(ϑ) curve around the crack constitutes a physically sound curve of the distribution of the total elastic strain-energy density there. Then, the critical T V,0- and T D,0- parameters control the failure behaviour of the material and, thus, the T- criterion can distinguish between failure by fracture or yielding. A study is made on the relative validity of the expected angle of crack propagation, especially in ductile materials. Different predictions are obtained from the T- criterion , as they are compared to those of an up-to-now popular criterion suitable only for brittle fractures. Experimental data show good agreement with the predictions of the T- criterion , especially for the critical stress for fracture.

球状黒鉛鋳鉄の溶接割れに関する研究 Ｉ インプラント試験による球状黒鉛鋳鉄の割れ感受性の評価

A study on the cracking susceptibility of nodular graphite cast irons by means of the implant test in different heat inputs is described. The implant test specimens were mainly smoothed 6 mm in diameter ones. Weld heat inputs, with the use of 4 nun diameter DFCNiFe type electrode (55%Ni-Fe), were changed 18, 000, 21, 000 and 24, 000 joules/cm with 10 cm/min travel speed and 50 mm bead length. After welding, when the temperature of the HAZ cooled to about 400°C, the load was applied.The implant specimens were fractured at about 100°C, which was below the Ms temperature of the cast irons used. In the heat input variation range of present work when heat input was made higher, the lower critical stress of fracture slightly inrceased; but it went up to only below a half of the strength of the base metal. The implant specimens were fractured at the part of the martensite structure with the highest micro-vickers hardness number, about 900. The fracture surface consisted of mainly intergranular fractures with partly quasi-cleavage fracture mode.

Study of the critical fracture stress of steel in uniaxial tension

1. A necessary and sufficient condition for avalanche fracture of the tough microcleavage type at low temperature and with developed plastic strain in the neck is the attainment of the critical tensile stress σ1max during loading. This stress is equal to the microcleavage stress of the given structure and is the stress at which a nucleated submicrocrack becomes a Griffith crack and initiates fracture. 2. The resistance of microcleavage in the initial (undeformed) state is determined by structural parameters of the steel d and Kr. The change in this resistance during deformation depends on the strain-hardening parameters A and n. 3. The sharp drop in the true fracture stress Sk near the ductile-brittle transition temperature Tb and the strain dependence of the cold-shortness threshold are conditional upon the character of the change in the resistance of the steel to microcleavage with a change in strain. 4. The characteristic of avalanche tough fracture of steel Sk and parameters of the stress state in the neck j, L, and B can be used to determine the resistance of deformed steel to microcleavage Rmce without the attainment of the cold-shortness temperature in an experiment.

The cold upsetting and free surface ductility of some commercial steels

The results of three different upsetting tests on four commercial steels are presented. The specimen geometry is shown to have a marked effect on the free surface ductility. The so-called collar test obviates the need of a grid of lines on the free surface of the specimen from which the axial, ez, and hoop, egq, strains are usually determined. The collar test results in reduced fracture strains vis a vis those achieved when compressing a circular cylinder. Consequently fracture can be induced earlier when compressing more ductile materials. It is demonstrated that the fracture strains from the three different upsetting tests do not lie on a straight line fracture locus, as proposed by Kuhn. A knowledge of the egq-ez strain path can lead to an evaluation of the stress history on the equatorial free surface of an upset specimen. In turn the stress history permits the assessment of various ductile fracture criteria. Two models were examined in the present work, neither of which suited all the experimental data. A maximum shear stress fracture criterion appeared to be more appropriate for the present set of experiments. The deleterious effect of MnS inclusions on the fracture strains is exhibited by comparing the behavior of AISI 1045 and 1146 steels.