Deformation and fracture of paper during the in-plane fracture toughness testing--Examination of the essential work of fracture method

The essential work of fracture (EWF) method is applied to various machine-made papers. The deforming and fracturing processes of the paper samples during testing is analyzed by means of the thermographic observation. Plastic deformation zone appears in three ways when deep double edge notched tension specimens are strained under in-plane stress: i.e. 1. type (i)--appearing through whole the ligament in a vague manner and developing into a circular (or oval) zone even before or at the maximum load point; 2. type (ii)--appearing from notch tip and amalgamating into a circular (or oval) zone after the maximum load point; and 3. type (iii)--appearing from notch tip and not amalgamating into a circular (or oval) zone until the sheet failure. Specimens with small ligament length (L) are likely to belong to type (i), while those with large L to type (ii) & (iii). Among these three types, type (i) fulfills the original assumption of the EWF method best in terms of the complete ligament yielding before crack initiation. Thus the specific essential work of fracture determined using the linear relation of type (i) should be correct, although the estimated work is a little smaller than that from the linear relation of type (ii) & (iii).     

Study of the fracture toughness and fracture morphology of polybenzimidazole

Polybenzimidazole (PBI) is a relatively new polymeric material exhibiting unusual properties that are attributable to its aromatic-heterocyclic monomer structure. Owing to its high strength, stiffness and excellent stability in hostile chemical and thermal environments, PBI is being used increasingly in critical applications. As a result, understanding the failure mechanisms of the material is vital. This paper presents the results of a study of the fracture toughness and fracture morphology of polybenzimidazole. The standard compact tension specimen was used as the basic experimental specimen in this study. The fracture tests were performed in an Instron tensile testing machine. The effects of varying the loading rate, and the ratio of the initial crack length,a, to the ligament length,W, were investigated. The fracture surface morphology was examined using optical and scanning electron microscopy. The results of this study indicate that the precracking technique significantly affects the measured fracture toughness. Also, an increase in the loading rate causes a significant decrease in fracture toughness. Examination of the fracture morphology reveals that PBI fracture surfaces exhibit many of the characteristics expected of a tough engineering plastic.     

Temperature dependence of fracture stress in the brittle fracture region

The temperature dependence of the fracture stress of bcc metals in the brittle fracture region is examined. A model taking into account the effect of local plastic deformation of the crack tip on transition to brittle fracture is proposed. The model is then used to derive analytical expression for the temperature dependence of the fracture stress in the material with an initial crack or notch.Translated from Problemy Prochnosti, No. 11, pp. 57–62, November, 1991.     

On the applicability of orthotropic fracture theory to the fracture of CFRP laminates

The digital birefringent-coating (DBC) system and finite element method (FEM) were used to study the fracture behavior for laminates of carbonfiber reinforced plastics (CFRPs) containing a central crack. Different crack orientations in different unidirectionally reinforced specimens were tested. The results show that the orthotropic fracture theory cannot adequately describe the fracture behavior of the CFRP laminates. There-fore, the widely used orthotropic fracture theory needs to be re-examined in detail.     

Analysis of Hertzian indentation fracture in the framework of finite fracture mechanics

The concept of finite fracture mechanics which assumes the spontaneous formation of a small, yet finite, crack and employs as stress-based as well as an energetic criterion is applied to the problem of indentation fracture initiation in brittle solids. In evaluating the energetic part of the fracture criterion a semi-analytical and a numerical approach, the latter involving detailed finite element simulations, are compared. The functionality of the hybrid (two-part) criterion in application to indentation fracture is analyzed in principle and, moreover, its predictive capabilities are illustrated by comparison with experimental findings.     

Estimation of fracture energy from the work of fracture and fracture surface area: I. Stable crack growth

Past attempts to determine fracture energy by the work of fracture (γ _WOF) technique, in most cases, have resulted in greater estimates due to the use of the cross-sectional area rather than the actual area of the fracture surface in calculations. The actual fracture surface area A _F of soda-lime-silica glass chevron-notch flexure specimens was estimated using atomic force microscopy. An equation for A _F was developed using the data from these tests. The use of A _F in the equation for γ _WOF resulted in γ _WOF values less than values reported from traditional fracture mechanics tests and from those obtained using the cross-sectional area. The implication is that the tortuosity of the fracture surface contributes to the energy expended during fracture and should be accounted for in the calculation of the fracture energy. These calculations provide an estimate for the minimum energy required to break bonds in the fracture process.     

Experimental research on the compressive fracture toughness of wing fracture of frozen soil

It is commonly found that not only bending fracture but also compressive fracture occur frequently in compression, furthermore, in some specific conditions, compressive fracture sometimes has dominant effect on frozen soil. Therefore, it is extremely necessary to study the mechanical characteristics of the compressive fracture of frozen soil and to investigate the damage and fracture mechanism of frozen soil based on the previous research on frozen soil damage in compression. This study draws on the ideas and methods used in compression fracture research on ice that is very similar to frozen soil, and specific clay in Shenyang region was adopted as the experimental material, to make compressive specimens containing tilted wing crack of different angles, and uniaxial unconfined compression fracture experiments were conducted at different temperatures and loading rates. The fracture toughness K_IC and K_IIC of the main crack tip of the specimens are calculated with obtained experimental results and the law of K_IC and K_IIC changing with tilted angles, temperatures and loading rate is obtained to gain an insight to damage mechanism of frozen soil in compression. This paper presents a meaningful attempt for the research on compressive fracture of frozen soil, so as to better solve practical engineering problems.     

The application of fracture mechanics to concrete and the measurement of fracture toughness

Summary The failure of concrete in uniaxial compression and tension is explained in terms of the energy concepts of fracture mechanics, and the difficulties associated with the measurement and evaluation of concrete “fracture toughness” are discussed. Basic assumptions relating to slow crack growth, stress concentration because of notch and value of E to be adopted for the calculation of the fracture toughness parameters are proposed. The effect of these assumptions on the values of critical strainenergy release rate and critical stress intensity factor are reported together with the trend of values with changes in concrete properties.

---

Résumé On traduit par les concepts énergétiques de la mécanique de la rupture la rupture du béton en compression et traction uniaxiales; les difficultés de mesure et d'évaluation de la résilience sont alors examinées. On propose des hypothèses de base en relation avec la fissuration progressive, la concentration des contraintes par effet d'entaille et la valeur de E à adopter pour le calcul des paramètres de la résillience. On montre l'effet de ces hypothèses sur l'évaluation de la vitesse de libération de l'énergie de déformation et sur le facteur d'intensité de la contrainte critique, ainsi que l'évolution des valeurs trouvées avec les modifications des propriétés du béton.

     

Impact of the anisotropy of fracture toughness on the propagation of planar 3D hydraulic fracture

Sedimentary rocks often exhibit a transverse isotropy due to fine scale layering. We investigate the effect of the anisotropy of fracture toughness on the propagation of a planar 3D hydraulic fracture perpendicular to the isotropy plane: a configuration commonly encountered in sedimentary basins. We extend a fully implicit level set scheme for the simulation of hydraulic fracture growth to the case of anisotropic fracture toughness. We derive an analytical solution for the propagation of an elliptical hydraulic fracture in the toughness dominated regime—a shape which results from a particular form of toughness anisotropy. The developed numerical solver closely matches this solution as well as classical benchmarks for hydraulic fracture growth with isotropic toughness. We then quantify numerically the transition between the viscosity dominated propagation regime at early time—where the fracture grows radially—to the toughness dominated regime at large time where the fracture reaches an elliptical shape in the case of an elliptical anisotropy. The time scale at which the fracture starts to deviate from the radial shape and gets more elongated in the direction of lower toughness is in accordance with the viscosity to toughness transition time-scale for a radial fracture defined with the largest value of fracture toughness. Similarly, the toughness dominated regime is fully reached along the whole fracture front when the time gets significantly larger than the same transition time-scale defined with the lowest value of toughness. Using different toughness anisotropy functions, we also illustrate how the details of the complete variation of fracture toughness with propagation direction governs the final hydraulic fracture shape at large time. Our results highlight toughness anisotropy as a possible hydraulic fracture height containment mechanism as well as the need for its careful characterization beyond measurements in the sole material axes (divider and arrester) directions.     

On the fracture of constrained layers

The problem of a crack embedded in a layer sandwiched between two elastic adherends is analysed accounting for the influence material property mismatch on the crack tip plastic deformation, which is contained in the layer. The cohesive crack model developed by Dugdale and Barrenblatt is adopted to model the strip yielding behaviour in a constrained layer. It is found that, due to the constraint imparted by elastic adherends with higher moduli, the near tip plastic deformation exhibits a sharp transition (plastic zone grows faster than the square of stress intensity factor) from small scale to large scale yielding. Because the region of singularity dominance for a crack embedded in a layer is generally much smaller than the layer thickness when the layer has a modulus much lower than the adherends, the prevailing failure mode of most bonded joints should be under large scale yielding conditions. A model based on energy balance is proposed to determine the fracture energy of bonded joints under such condition, taking into account of the plastic dissipation in the constrained layer. Comparison with experimental results demonstrates that the theory correctly predicts the dependence of fracture toughness on layer thickness as observed in experiments. This revised version was published online in July 2006 with corrections to the Cover Date.     

Modelling the fracture of cementitious materials

The crack band and the fictitious crack line models of the fracture process zone in cementitious materials are discussed. The two methods are quite similar. However, the fictitious crack model is shown to lend itself to a simple K-superposition method which makes use of known analytical expressions. This method is shown to give very similar results to a finite-element analysis of the fictitious crack model and has the advantage that it can be programmed for a personal computer. The predictive capability of the fictitious crack model is demonstrated by comparison of the experimental load-deflection curve for a small notch bend mortar specimen with a theoretical curve calculated from data obtained from larger beams. It is suggested that the RILEM test method for the determination of the fracture energy should be used also to establish a bilinear stress-displacement relationship for the strain-softening of the fracture process zone.     

On the statistical nature of fracture

This paper explores the statistical nature of the mechanisms of fracture in structural materials and the loads that initiate them. The result of employing either a weak link or bundle model in the application of statistics to problems of fracture is examined. Experimental data is presented for the fracture of metal chains and the fracture of sheet aluminum containing machined cut-outs and cracks. The scatter in fracture loads for the chains and fracture toughness for the sheet specimens is statistically analyzed utilizing four statistical distributions: normal, lognormal, extreme value, and two-parameter Weibull functions. Based upon this work there appears to be no general a priori justification to utilize either the weak link or the bundle model in the statistical assessment of the fracture of typical engineering structural components.     

On the fracture kinetics of solids

A simple model is considered in order to investigate the kinetics of fracture in polymers, with special reference to quantum effects which may occur even at room temperature.

---

Zusammenfassung An Hand eines einfachen Modells wird die Bruchkinetik in Polymeren untersucht. Die Quanteneffekte, welche sogar schon bei Raumtemperatur auftreten können, werden besonders herausgestellt.

---

Résumé Pour l'étude de la cinétique de la rupture dans les polymères, on a considéré un modèls simple à l'aide duquel on a fait apparaître des effets quantiques qui peuvent survenir même a température ambiante.

     

On the environmental fracture of polymethylmethacrylate

Crack propagation of PMMA in some liquid environments is described for various testing conditions, such as fixed load, fixed displacement and monotonically increasing displacement. Fracture mechanics concepts have been used successfully in analysing the results. When continuous stable cracking is achieved, values of fracture toughness (R) for PMMA under these loading conditions are obtained as a function of crack velocity () using the method of Gurney and Hunt [11]. For crack velocities greater than 10^–2 mm sec^–1, the fracture toughness values in the environments are increased when compared with the corresponding air results. Unique relationships betweenR and have been shown to exist for cracking in ethanol and carbon tetrachloride.     

On the pop-in mode of fracture

Experimental observations concerning the pop-in mode of fracture obtained during an investigation of the fracture toughness of glassy plastics are related. Comments on the mechanics of the pop-in mode are presented.