Showing papers on "Fracture toughness published in 1982"

Mechanics of Transformation‐Toughening in Brittle Materials

Abstract: Particles which undergo a stress-induced martensitic transformation are known to toughen certain brittle materials. The enhanced toughness can be considered to originate from the residual strain fields which develop following transformation and tend to limit the crack opening. The increased toughness can estimated from the crack-tip stress-intensity change induced by the transformation of a volume of material near the crack tip. It is found that the initial zone, prior to crackgrowth, provides no change in stress intensity. As the crack grows, the zone (associated with a positive transformation strain) induces a stress-intensity reduction that rises to a maximum level after some crack propagation. The influence of particle-size distribution on the stress-intensity reduction is also discussed.

Elastic/Plastic Indentation Damage in Ceramics: The Lateral Crack System

Abstract: The mechanics of lateral crack propagation in a sharp-indenter contact field are described. The driving force for fracture has its origin in the residual component of the elastic/plastic field, which becomes dominant as the indenter is unloaded. Expressions for equilibrium crack evolution are derived, with due allowance for the close proximity of crack plane and specimen free surface. As with the median/radial crack system considered in an earlier paper, the ratio hardness-to-modulus complements toughness in the fracture relations. The basic predictions of the theory are examined in terms of experimental measurements of lateral crack dimensions in materials with a wide range of mechanical properties. The prospects of predicting the extent of lateral fracture in other ceramics, and thence of establishing a base for analyzing such important practical properties as surface erosion, are discussed.

Silicon carbide fibre reinforced glass-ceramic matrix composites exhibiting high strength and toughness

Abstract: Silicon carbide fibre reinforced glass-ceramic matrix composites have been investigated as a structural material for use in oxidizing environments to temperatures of 1000° C or greater. In particular, the composite system consisting of SiC yarn reinforced lithium aluminosilicate (LAS) glass-ceramic, containing ZrO2 as the nucleation catalyst, has been found to be reproducibly fabricated into composites that exhibit exceptional mechanical and thermal properties to temperatures of approximately 1000° C. Bend strengths of over 700 MPa and fracture toughness values of greater than 17 MN m−3/2 from room temperature to 1000° C have been achieved for unidirectionally reinforced composites of ∼ 50 vol% SiC fibre loading. High temperature creep rates of 10−5 h−1 at a temperature of 1000° C and stress of 350 MPa have been measured. The exceptional toughness of this ceramic composite material is evident in its impact strength, which, as measured by the notched Charpy method, has been found to be over 50 times greater than hot-pressed Si3N4.

A geometric model for fatigue crack closure induced by fracture surface roughness

Abstract: Mechanisms for fatigue crack closure under plane strain conditions have recently been identified at very low (near-threshold) stress intensities in terms of effects of excess corrosion deposits or fracture surface roughness in promoting premature closure of the crack. In the present paper, a geometric model is presented for crack closure induced by fracture surface roughness. This model specifically addresses the contribution from both Mode I and Mode II crack tip displacements in addition to considering the nature of the fracture surface morphology. The implications of this model are briefly discussed in light of the roles of grain size, yield strength, microstructure, and crack size in influencing near-threshold fatigue behavior in engineering alloys.

Transformation toughening: Part 4 Fabrication, fracture toughness and strength of Al2O3-ZrO2 composites

Abstract: Three Al2O3-ZrO2 composite series, containing 0, 2 and 7.5 mol % Y2O3, were fabricated for fracture toughness determinations. Without Y2O3 additions, tetragonal-phase ZrO2 could only be retained up to approximately 10 vol % ZrO2; additions of 2 mol % Y2O3 allowed full retention of the tetragonal phase up to 60 vol % ZrO2. Cubic ZrO2 was produced with additions of 7.5 mol % Y2O3. Significant toughening and strengthening was achieved when tetragonal ZrO2 was present.

Critical Microstructures for Microcracking in Al2O3‐ZrO2 Composites

Abstract: The internal strains asSociated with the martensitic phase transformation of zirconia were used to introduce microcracks into Al2O3/ZrO2 composites. The degree of transformation was found to be dependent on the volume fraction of ZrO2 and its size, the latter of which could be controlled by suitable heat treatments. The microstructural changes that occurred during the heat treatments were studied using quantitative microscopy and X-ray diffraction. For materials containing more than 7.5 vol% Zr02, the ZrO2 particles were found to pin the Al2O3 grain boundaries, thus limiting the Al2O3 grain growth. The limiting grain size was found to be dependent on size and volume fraction of ZrO2. Heat treatments for the higher volume fraction materials (>7.5 vol% ZrO2) caused micro-structural changes which resulted in increased amounts of monoclinic ZrO2 at room temperature; elastic modulus measurements indicated that this was occurring concurrently with microcracking. By combining the ZrO2 grain-size distributions with the X-ray analysis it was possible to calculate the critical ZrO2 size required for the transformation. The critical size was found to decrease with increasing amounts of ZrO2. Hardness and indentation fracture toughness were measured on the composites. Grain fragmentation was observed at the edge of the indentations and microcracks were observed directly, using an AgNO3 decoration technique, near the indentations.

Interlaminar Fracture of Composite Materials

Abstract: Interlaminar fracture characteristics of a graphite/epoxy composite material (AS1/3501-6) are investigated under the opening, shearing and mix ed mode conditions. The Arcan test fixture was modified to accomodate the composite specimen containing an embedded interlaminar crack. Both critical stress intensity factor and strain energy release rate data were deter mined and the quadratic interaction for mixed mode behavior was compared to experimental data. Results of over sixty tests showed that the test fixture yielded results which compare favorably with results from contemporary test fixtures. Critical fracture parameters for the opening and shearing modes were shown to differ by a factor of 9.1. Further, the test results showed general agreement with the quadratic interaction relation.

The influence of microstructure and strength on the fracture mode and toughness of 7XXX series aluminum alloys

Abstract: The effects of microstructure and strength on the fracture toughness of ultra high strength aluminum alloys have been investigated. For this study three ultra high purity compositions were chosen and fabricated into 1.60 mm (0.063 inches) sheet in a T6 temper providing a range of yield strengths from 496 MPa (72 ksi) to 614 MPa (89 ksi). These alloys differ only in the volume fraction of the fine matrix strengthening precipitates (G. P. ordered + η′ ). Fracture toughness data were generated using Kahn-type tear tests, as well asR-curve andJ c analyses performed on data from 102 mm wide center cracked tension panel tests. Consistent with previous studies, it has been demonstrated that the toughness decreases as the yield strength is increased by increasing the solute content. Concomitant with this decrease in toughness, a transition in fracture mode was observed from predominantly transgranular dimpled rupture to predominantly intergranular dimpled rupture. Both quantitative fractography and X-ray microanalysis clearly demonstrate that fracture initiation for the two fracture modes occurred by void formation at the Cr-dispersoids (E-phase). In the case of intergranular fracture, void coalescence was facilitated by the grain boundary η precipitates. The difference in fracture toughness behavior of these alloys has been shown to be dependent on the coarseness of matrix slip and the strength differential between the matrix and precipitate free zone (σM-σPFZ). A new fracture mechanism has been proposed to explain the development of the large amounts of intergranular fracture observed in the low toughness alloys.

Dependence of Fracture Toughness of Alumina on Grain Size and Test Technique

Abstract: The fracture toughness (KIc) of sintered alumina was measured using notched beam (NB) and indentation/strength-in-bending (ISB) techniques. KIc (NB) decreases with increasing grain size. For fine-grained materials (<5 μm), NB results overestimate KIc, and exhibit a substantial notch-radius sensitivity. A stress-intensity-derived model is used to explain this notch sensitivity. The ISB results are very similar to those obtained using the double-cantilever-beam (DCB) method and show an increasing fracture toughness with increasing grain size. The differences between the NB and ISB (DCB) results for coarser-grained materials are thought to be related to R-curve behavior.

Transformation toughening: Part 2 Contribution to fracture toughness

Abstract: AbstractTwo approaches are taken to determine the contribution of a stress-induced phase transformation to the fracture toughness of a brittle material. Both approaches result in an expression for the critical stress intensity factor,Kc, of $$K_c = \\left[ {K_0^2 + \\frac{{2RE_c V_i (|\\Delta G^c | - \\Delta U_{se} f)}}{{(1 - v_c^2 )}}} \\right]^{1/2} ,$$ whereK0 is the critical stress intensity for the material without the transformation phenomenon, (¦ΔGc¦−Usef) is the work done per unit volume by the stress field to induce the transformation,Ec andνc are the elastic properties,Vi is the volume-fraction of retained, high-temperature phase andR is the size of the transformation zone associated with the crack. It is assumed that only those inclusions (or grains) close to the free surface of the crack will contribute to the fracture toughness; thus,R the inclusion size. The chemical free-energy change associated with the transformation, ¦ΔGc¦, will govern the temperature and alloying dependence of the fracture toughness.

Transformation toughening: Part 5 Effect of temperature and alloy on fracture toughness

Abstract: The critical stress-intensity factor,Kc, of materials containing tetragonal ZrO2 was found to decrease with increasing temperature and CeO2 alloying additions, as predicted by theory. The temperature dependence ofKc was related to the temperature dependence of the chemical free-energy change associated with tetragonal-monoclinic transformation. Good agreement with thermodynamic data available for pure ZrO2 was obtained when the size of the transformation zone associated with the crack was equated to the size of the ZrO2 grains. TheKc against CeO2 addition data was used to estimate the tetragonal, monoclinic, cubic eutectoid temperature of 270° C in the ZrO2-CeO2 binary system.

Stress Intensity Factors, Crack Profiles, and Fatigue Crack Growth Rates in Residual Stress Fields

Abstract: A linear elastic fracture mechanics approach to crack growth rate prediction implies the need to calculate accurate, effective stress intensity (K) factors, and hence effective R-values, (K m i n /K m a x ), for components containing residual stress. To this end the weight function and associated superposition techniques are described, with emphasis on stress intensity and crack shape prediction for residual stress problems. Stress intensity factors are presented for various geometries with residual stress fields. The nonlinear, crack surface 'overlapping' effect is noted, and the case of cracks emanating from notches in residual stress fields is shown to be an associated problem. The application of such results in crack growth rate prediction is addressed. The characteristic crack growth rate features of several different loading systems are predicted, and shown to agree with available experimental data. Finally, the qualitative changes in the form of standard S-N curves for welded details are predicted, and shown to conform with limited available S-N curve experimental data.

Critical stress in silicon brittle fracture, and effect of ion implantation and other surface treatments

Abstract: We introduce a method, which is free of specimen edge effect, for the determination of critical stress in material brittle fracture. Using this method, we have investigated the critical stress in silicon brittle fracture. Silicon wafers polished with silica gel showed an average fracture stress of 2.8 GPa, with a standard deviation of 1.2 GPa and a maximum observed value of 6.9 GPa. We have also investigated effects of various surface treatments on the critical stress. Mechanically lapped surfaces, with damage penetrating deeper than ∼3 μm, reduced the fracture strength to 0.3–0.4 GPa (damage surface placed in tension). Both polysilicon and quartz overlays reduced the silicon fracture strength only very slightly, while argon implantation (at 150 keV, with a dose of 1×1016 cm−2) did not show a detectable effect. However, anneal of the argon implanted samples at 900 °C in nitrogen for one hour significantly increased the silicon fracture strength, conceivably as a consequence of the removal of existing surface flaws by an epitaxial regrowth of the implantation‐amorphized surface layer. The last finding is both of basic interest and of practical significance. Silicon wafers of (100) orientation showed a ∼50% higher fracture strength than wafers of (111) orientation.

Dislocation‐free zone model of fracture comparison with experiments

Abstract: The dislocation‐free zone (DFZ) model of fracture has been extended to study the relationship between the stress intensity factor, extent of plastic deformation, and crack tip geometry of an elastic‐plastic crack as a function of applied stress. The results show that the stress intensity factor K decreases from the elastic value at first slowly, then goes rapidly to zero as the number of dislocations in the plastic zone increases. The crack with a zero stress intensity factor has its crack tip stress field completely relaxed by plastic deformation and hence is called a plastic crack. Between the elastic and plastic cracks, a wide range of elastic‐plastic cracks having both a stress singularity and a plastic zone are possible. These elastic‐plastic cracks with a DFZ are predicted if there is a critical stress intensity factor Kg required for the generation of dislocations at the crack tip. The expression for Kg is obtained from the crack tip dislocation nucleation model of Rice and Thomson. In most metals,...

Temperature Dependence of Strength and Fracture Toughness of ZrO2 Single Crystals

Abstract: Results of strength and fracture–toughness tests on single crystals of partially stabilized ZrO2 at temperatures above and below the tetragonal–monoclinic transformation temperature are reported. The temperature dependence of toughening mechanisms is discussed with respect to theories for phase–transformation toughening and other toughening mechanisms.

Mixed mode plane stress ductile fracture

Abstract: Mixed mode ductile fractures in thin sheets are shown to be possible. The staggered deep edge notch tension specimen enablesJ p , the plane stress propagation value of theJ integral, and dJ/dα, the rate of increase inJ with crack growth to be measured from the specific work of fracture. TheJ integral can also be separated into its two component modesJ 1 andJ n. For the particular low alloy steel testedJ p is virtually independent of the mode of fracture, but for other materialsJ p may be dependent on the fracture mode.

Optical Measurement of the Plastic Strain Concentration at a Crack Tip in a Ductile Steel Plate

Abstract: The shadow spot method has been established as a valuable experimental procedure for measuring elastic stress intensity factors in planar fracture specimens. It is noted here that if the crack-tip deformation field in specimens of ductile materials can be characterized by means of a single plastic intensity factor, analogous to the stress intensity factor in linear elastic fracture mechanics, then the shadow spot method has potential for use in measuring this intensity factor. The value of the J-integral is adopted as the plastic strain intensity factor, and the lateral contraction of an elastic-ideally plastic planar specimen is calculated in terms of J from the nonhardening limit of the HRR asymptotic field of elastic-plastic fracture mechanics. The theoretical caustic curve which would be generated by geometrical reflection of normally incident parallel light from points of the deformed specimen surface lying well within the plastic zone is determined, and it is shown that the value of J is proportional to the maximum transverse diameter of the shadow spot to the third power. Results of preliminary experiments, in which values of J for a given single edge notched steel plate specimen are inferred from measurements peformed separately from the elastically and plastically deforming parts of the specimen, are also reported.

The influence of inertia on elastic-plastic antiplane-shear crack growth

Abstract: Results of a study of steady-state antiplane-shear crack growth in an elastic ideally-plastic material are reported. First, an exact expression for the distribution of strain on the crack line within the primary active plastic zone is obtained. It is shown that the expression reduces to the correct asymptotic form for the special case of vanishingly small distance from the crack tip for any nonzero crack growth speed, and it reduces to the correct limit as the crack speed approaches zero for any point on the crack line. Then, the full elastic-plastic deformation field is determined under the conditions of small-scale yielding by means of the numerical finite element method. The computed strain distribution on the crack line is found to compare closely with the analytical result for this distribution. Finally, the analytical and numerical results are combined with the “critical plastic strain at a characteristic distance” crack growth criterion to generate theoretical fracture toughness vs crack speed relationships. The results are similar to experimentally observed fracture toughness vs crack speed relationships. In particular, the results show a strong dependence of fracture toughness on crack speed for even moderate crack growth rates. Because the material response is independent of strain-rate, this suggests that the influence of inertia on the fracture resistance of the material is significant.

Compliance calibration of the short rod chevron-notch specimen for fracture toughness testing of brittle materials

Abstract: The short rod chevron-notch specimen has the advantages of (1) crack development at the chevron tip during the early stage of test loading and (2) convenient calculation of KIc from the maximum test load and a calibration factor which depends only on the specimen geometry and manner of loading. For generalized application, calibration of the specimen over a range of specimen proportions and chevron-notch configurations is necessary. Such was the objective of this investigation, wherein calibration of the short rod specimen was made by means of experimental compliance measurements converted into dimensionless stress intensity factor coefficients.

The fracture toughness of dental composites. II. The environmental and temperature dependence of the stress intensification factor (KIC).

Abstract: Summary A fracture mechanics approach has been adopted to quantify the failure of dental composites under stress. The parameter KIC has been determined by the use of SEN specimens subject to the variables of composite product type, storage environment, test environment and temperature, and polymerization time. The results show that KIc varies from product to product, increasing significantly if there is sufficient time for the absorption of storage water. The effect of test environment and temperature (over the range expected in vivo) is minor.

Grain‐Size Dependence of Fracture Energy in Ceramics

Abstract: A simple model incorporating thermal elastic anisotropy stresses is used to calculate the microcrack zone size around cracks in Al2O3. It is found that the ratio of microcrack zone size to grain size is almost constant for notched beam tests, but increases with grain size for double cantilever beam data. It is suggested that notched-beam ratios of fracture toughness are related to crack initiation, whereas double cantilever beam values are related to propagation and reflect R-curve behavior of the material.

Application of the principles of linear fracture mechanics to the composite materials

Abstract: Application of the principles of linear fracture mechanics to the orthotropic composite materials is examined. It is shown that fracture toughness of unidirectional composites is independent of crack length but dependent on crack-fiber orientation. For experimental verification of the above principles, uni-directional glass epoxy material (Scotchply 1002) was used. The fracture toughness of Scotchply 1002 for different crack-fiber orientations is obtained by utilizing Solid Sap finite element program and compact tension specimens. An empirical formula relating the fracture toughness of the material for different crack-fiber orientation is found.

Carbon fibre-reinforced silicon nitride composite

Abstract: The processing of silicon nitride reinforced with carbon fibre was studied. The problems of physical and chemical incompatibility between carbon fibre and the silicon nitride matrix were solved by addition of a small amount of zirconia to the matrix and by low-temperature hot-pressing. The composite material possesses a much higher toughness than hot-pressed silicon nitride. Its work of fracture increased from 19.3 J m−2 for unreinforced Si3N4, to 4770 J m−2; its fracture toughness,K lc , increased from 3.7 MN m−3/2 for unreinforced material, to 15.6 MN m−3/2. The strength remains about the same as unreinforced Si3N4 and the thermal expansion coefficient is only 2.51×10−6 ° C−1 (RT to 1000° C). It is anticipated that this composite may be promising because of its mechanical and good thermal shock-resistance properties.