Showing papers on "Fracture toughness published in 2000"

Numerical experiments in revisited brittle fracture

Abstract: The numerical implementation of the model of brittle fracture developed in Francfort and Marigo (1998. J. Mech. Phys. Solids 46 (8), 1319–1342) is presented. Various computational methods based on variational approximations of the original functional are proposed. They are tested on several antiplanar and planar examples that are beyond the reach of the classical computational tools of fracture mechanics.

Structural basis for the fracture toughness of the shell of the conch Strombus gigas

Abstract: Natural composite materials are renowned for their mechanical strength and toughness: despite being highly mineralized, with the organic component constituting not more than a few per cent of the composite material, the fracture toughness exceeds that of single crystals of the pure mineral by two to three orders of magnitude The judicious placement of the organic matrix, relative to the mineral phase, and the hierarchical structural architecture extending over several distinct length scales both play crucial roles in the mechanical response of natural composites to external loads Here we use transmission electron microscopy studies and beam bending experiments to show that the resistance of the shell of the conch Strombus gigas to catastrophic fracture can be understood quantitatively by invoking two energy-dissipating mechanisms: multiple microcracking in the outer layers at low mechanical loads, and crack bridging in the shell's tougher middle layers at higher loads Both mechanisms are intimately associated with the so-called crossed lamellar microarchitecture of the shell, which provides for 'channel' cracking in the outer layers and uncracked structural features that bridge crack surfaces, thereby significantly increasing the work of fracture, and hence the toughness, of the material Despite a high mineral content of about 99% (by volume) of aragonite, the shell of Strombus gigas can thus be considered a 'ceramic plywood' and can guide the biomimetic design of tough, lightweight structures

The Tip Region of a Fluid-Driven Fracture in an Elastic Medium

Abstract: The focus of this paper is on constructing the solution for a semi-infinite hydraulic crack for arbitrary toughness, which accounts for the presence of a lag of a priori unknown length between the fluid front and the crack tip. First, we formulate the governing equations for a semi-infinite fluid-driven fracture propagating steadily in an impermeable linear elastic medium. Then, since the pressure in the lag zone is known, we suggest a new inversion of the integral equation from elasticity theory to express the opening in terms of the pressure. We then calculate explicitly the contribution to the opening from the loading in the lag zone, and reformulate the problem over the fluid-filled portion of the crack. The asymptotic forms of the solution near and away from the tip are then discussed, It is shown that the solution is not only consistent with the square root singularity of linear elastic fracture mechanics, but that its asymptotic behavior at infinity is actually given by the singular solution of a semi-infinite hydraulic fracture constructed on the assumption that the fluid flows to the tip of the fracture and that the solid has zero toughness. Further, the asymptotic solution for large dimensionless toughness is derived, including the explicit dependence of the solution on the toughness. The intermediate part of the solution (in the region where the solution evolves from the near tip to the far from the tip asymptote) of the problem in the general case is obtained numerically and relevant results are discussed, including the universal relation between the fluid lag and the toughness.

Mechanical properties of new composite restorative materials.

Abstract: Objective: Determination of flexural strength, flexural modulus, fracture toughness, Vickers hardness, and wear resistance of condensable composites (Solitaire, Surefil, Alert) and an ormocer (Definite) in comparison with a hybrid composite (Tetric Ceram) and an ion-releasing composite (Ariston pHc). Methods: Flexural strength, flexural modulus, and fracture toughness were determined in 3-point bending. Single-edge notched-bend specimens were used to evaluate fracture toughness. Microhardness was measured with a Vickers indenter. Wear was determined in a pin-on-block-design with a Degusit antagonist at 50 N load and quantified by a replica technique after 6000, 10000, 30000, and 50000 load cycles using a 3D-laser scanner. All results were statistically analyzed with ANOVA and post hoc Tukey HSD tests. Results: Alert exhibited the highest flexural modulus, KIC, and hardness, but lowest wear resistance. Solitaire presented the highest wear resistance, but significantly lower flexural strength, flexural modulus, KIC, and hardness than all other materials. No significant correlation could be detected between hardness and wear of the tested composites with Pearson's correlation coefficient. Significance: The condensable composites differed significantly in their mechanical properties. This study suggested that, besides the filler content level and filler size, other factors like matrix-filler interactions highly influence the fracture and wear behavior of the materials. © 2000 John Wiley & Sons, Inc. J Biomed Mater Res (Appl Biomater) 53: 353–361, 2000

Size eÄect on toughness induced by crack close to free surface

Abstract: This study explains from the fracture mechanics principles that the common size e•ect observed in fracturetoughness and energy measurements of many engineering materials including concrete, fiber reinforced compositesand even coarse-grained ceramics are in fact similar to what has been observed in the well-studied elastic–plasticfracture of metals. The conditions required for measurements of the material constant, the plane strain fracturetoughness K IC , of metals are akin to those required to avoid such a size e•ect on the fracture toughness and energyof concrete and other composites. Using the common yield strength and plain strain fracture toughness criteria areference crack length a is defined in this study, which is then used to introduce a simple asymptotic function. Theasymptotic analysis shows that the size e•ect on fracture toughness and energy of a heterogeneous material such asconcrete will be inevitable if the relative crack measured by the crack ratio a=a or the remaining ligament ratio–Wyaƒ=a is too close to one. This relative crack needs to be around 10 or even higher to avoid the size e•ectinfluence. Experimental results and previous models are compared with the current asymptotic analysis. # 2000Elsevier Science Ltd. All rights reserved.

Effect of Specimen Geometry and Testing Method on Mixed Mode I–II Fracture Toughness of a Limestone Rock from Saudi Arabia

Abstract: The effect of testing method and specimen geometry such as diameter, thickness, and crack length and type on measured fracture toughness was investigated using specimens collected from a limestone rock formation outcropping in the Central Province of Saudi Arabia. Straight Edge Cracked Round Bar Bend (SECRBB), semicircular disk specimens under three point bending, and Brazilian disk specimens under diametrical compression were used in this investigation. SECRBB specimens were used for the Mode-I study, and notched Brazilian disk and semicircular specimens were used for the mixed Mode I–II study. The results show that specimen diameter and crack type have a substantial influence on the measured fracture toughness; however, loading rate, crack size, and specimen thickness seem to have a negligible effect on the fracture toughness. Mode-I fracture toughness is significantly influenced by specimen diameter and crack type, while their effects on Mode-II fracture toughness are generally negligible. The different specimens (SECRBB, Brazilian disk, and semicircular) can give comparable results only when the proper span to diameter ratio is used. The Brazilian disk with a straight notch was found to be the most convenient geometry to use for fracture toughness determination. A simple method of making a precise notch inside the disk is presented, using the combination of a drilling machine and a wire saw.

Fracture toughness of polysilicon MEMS devices

Abstract: Polysilicon fracture mechanics specimens have been fabricated using standard microelectro-mechanical systems (MEMS) processing techniques, with characteristic dimensions comparable to typical MEMS devices. These specimens are fully integrated with simultaneously fabricated electrostatic actuators that are capable of providing sufficient force to ensure catastrophic crack propagation. Thus, the entire fracture experiment takes place on-chip, eliminating the difficulties associated with attaching the specimen to an external loading source. The specimens incorporate atomically sharp cracks created by indentation, and fracture is initiated using monotonic electrostatic loading. The fracture toughness values are determined using finite element analysis (FEA) of the experimental data, and show a median value of 1.1 MPa m 1/2 .

Deformation and fracture of aluminium foams

Abstract: The tensile and compressive properties and the fracture resistance of two aluminium alloy foams have been measured. The yield strength, unloading modulus and toughness increase with relative density in such a manner that the closed cell foams of this study behave as open cell foams. These relationships can be described adequately by power law fits. Experimental results, when compared with theoretical models based on idealised foam structures, reveal unexpected discrepancies. We conclude that they are caused by morphological defects in the microstructures of the foams, the effects of which were not included in the models. Tests on samples with deep sharp notches show that the tensile and compressive strengths are notch-insensitive. Fracture toughness measurements show an R-curve behaviour. This is analysed in terms of the underlying microstructure — the major cause of the R-curve was observed to be the development of crack bridging ligaments behind the crack tip. The compact tension specimens employed were sufficiently small for the uncracked ligaments to suffer plastic yielding during the fracture tests. The crack bridging response was quantified in terms of the normal traction versus plastic displacement curve; the area under this curve for a deep double edge-notched specimen is approximately equal to the measured steady state toughness. The accuracy of an existing micromechanical model for the fracture toughness of brittle open cell foams is assessed, and a new toughness model for ductile foams is derived.

Modeling of the competition between shear yielding and crazing in glassy polymers

Abstract: Fracture in amorphous glassy polymers involves two mechanisms of localized deformations: shear yielding and crazing. We here investigate the competition between these two mechanisms and its consequence on the material's fracture toughness. The mechanical response of the homogeneous glassy polymer is described by a constitutive law that accounts for its characteristic softening upon yielding and the subsequent progressive orientational strain hardening. The small scale yielding, boundary layer approach is adopted to model the local finite-deformation process in front of a mode I crack. The concept of cohesive surfaces is used to represent crazes and the traction-separation law incorporates craze initiation, widening and breakdown leading to the creation of a microcrack. Depending on the craze initiation sensitivity of the material, crazing nucleates at the crack tip during the elastic regime or ahead of the crack. As the crazes extend, plasticity develops until an unstable crack propagation takes place when craze fibrils start to break down. Thus, the critical width of a craze appears to be a key feature in the toughness of glassy polymers. Moreover, the opening rate of the craze governs the competition between shear yielding and brittle failure by crazing.

Energy dissipation and path instabilities in dynamic fracture of silicon single crystals

Abstract: Brittle fracture usually proceeds at crack driving forces which are larger than those needed to create the new fracture surfaces. This surplus can lead to faster crack propagation or to the onset of additional dissipation mechanisms. Dynamic fracture experiments on silicon single crystals reported here show several distinct transitions between different dissipation mechanisms. Cleavage fracture is followed by the propagation of a faceted crack front, which is finally followed by a path instability and the propagation of multiple cracks. The fracture surface qualitatively corresponds to the mirror, mist, and hackle morphology of amorphous materials. However, the corresponding fracture mechanisms, which remain largely unknown in the amorphous materials, can clearly be identified here.

New aspect of development of high strength aluminum alloys for aerospace applications

Abstract: New aspect of developing the materials in lights of interrelationship among alloy/process microstructure (mainly the second phase particles) — properties combined with micromechanics has been carried out in 2024 aluminum alloys. The fracture toughness is proportional to the square root of the spacing of constituents, Cu 2 FeAl 7 , in 2024 aluminum alloys. Broadening the spacing 75–140 μm, the fracture toughness increases by 20%. In a low Δ K region, the fatigue cracks propagate much slowly by broadening the spacing of dispersoids, Cu 2 Mn 3 Al 20 . Broadening the spacing, the crack propagation rate decreases by 50%. The larger size of dispersoids, Cu 2 Mn 3 Al 20 , makes the rate much slower than smaller ones, Cr 2 Mg 3 Al 18 or ZrAl 3 . On the other hand, in a high Δ K region, the rate becomes slower mainly by broadening the constituents spacing. The newly developed 2×24 aluminum alloy sheets, in these concepts in mind, have excellent fracture toughness and fatigue crack propagation characteristics to provide lower weight, higher damage tolerance, and longer-term durability for aerospace applications.

A new criterion for internal crack formation in continuously cast steels

Abstract: To estimate the cracking condition in continuously cast steels, a new model for critical fracture stress given from the measured critical strain has been proposed, which can take into account the brittle temperature range and strain rate. The effects of brittle temperature range and strain rate on critical strain for internal crack formation were analyzed. When the brittle temperature range and strain rate were increased, the possibility of internal crack formation increased due to the decreasing critical strain. To describe the thermomechanical property model of the mushy zone between zero strength temperature (ZST) and zero ductility temperature (ZDT), the yield criterion for porous metals, which can take into account δ/γ transformation, was used. Using the fitting equation for the measured critical strain and the microsegregation analysis, the thermomechanical behavior of the mushy zone could be successfully described by the proposed model, which incorporates the effects of microsegregation of solute elements and δ/γ transformation on hot tear during solidification at the given range of steel compositions and strain rates. A cracking criterion based on the difference of deformation energy in the brittle temperature range is proposed to explain the cracking phenomenon of whole carbon range.