Finite Size Specimen Research Articles

Size effect on elastic properties of random composites

In addition to the prediction of effective elastic properties of random media, the statistical variations of these properties for finite size specimens are of practical interest. From finite element method calculations on simulated 2D random media, size effects are studied and modelled. They enable us to draw practical conclusions for finite element applications to elastic random media.

Maximum-Load Predictions in the Dugdale Model Using a Critical CTOA Criterion

Abstract An engineering method of elastic-plastic fracture analysis is suggested for plane-strain specimens under tension. The condition for an increment of crack extension is set by a critical increment of crakc tip opening displacement (CTOD). The CTOD increment divided by the incremental crack extension is a critical crack tip opening angle (CTOA), assumed to be constant for a material of a given thickness, characterizing the tearing resistance of material. Based on a finite-element analysis of crack tip deformation, a load term in the CTOD equation of the Dugdale strip yield model is modified to accommodate large and small scale yielding, for which cohesive stress in the strip is assumed greater than that for the plane-stress model Approximate generalization of the Dugdale model is suggested for finite-size specimens. A definition of CTOD is reviewed with a round and sharp crack tip. In a successive application of the CTOA criterion at a current extending crack tip, the integration of the incremental crack extensions and load increments after fracture mitration gives a relationship in which a maximum load is either a peak load or a limit load on an unbroken ligament. Material constants are evaluated so that the calculated loads agree with test loads at each crack extension. The proposed method is applied to various specimens of 304 stainless steel for which test data are available.

Stability Analysis of Bridged Cracks in Brittle Matrix Composites

The bridging of matrix cracks by fibers is an important toughening mechanism in fiber-reinforced brittle matrix composites. This paper presents the results of a nonlinear finite element analysis of the Mode I propagation of a bridged matrix crack in a finite size specimen. The composite is modeled as an orthotropic continuum and the bridging due to the fibers is modeled as a distribution of tractions that resist crack opening. A critical stress intensity factor criterion is employed for matrix crack propagation, while a critical crack opening condition is used for fiber failure. The structural response of the specimen (load-deflection curves) as well as the stress intensity factor of the propagating crack is calculated for various constituent properties and specimen configurations for both tensile and bending loading. By controlling the length of the bridged crack, results are obtained that highlight the transition from stable to unstable behavior of the propagating crack.

Interface fracture and viscoelastic deformation in finite size specimens

In the small scale yielding limit, the viscoelastic energy dissipation and the predicted fracture toughness of the interface between two viscoelastic polymers are monotonically increasing functions of the crack growth rate. For a finite size specimen however such prediction are no longer strictly valid. We demonstrate here that there is a maximum viscoelastic energy dissipation (and thus fracture toughness) at a characteristic interface crack velocity which depends not only on the micromechanical properties of the interface and the viscoelastic properties of the bulk polymers but also upon the specimen dimensions. Our analytical results allow us to deduce G=Gad[1+φ(aTȧ,c)] which relates the experimental fracture toughness to the intrinsic fracture toughness of the interface Gad, the WLF shift factor aT and c, a dimensionless parameter which is a function of the micromechanical properties of the interface, the mechanical properties of the polymers and the specimen dimensions. This result is similar to an empirical relation developed to fit experimental results; this relation however was assumed to be independent of c (specimen geometry). We demonstrate that the dependence of φ on c is substantially weaker than its dependence on aTȧ, which accounts for the success of the empirical relation in correlating the experimental data.

Dominant Creep Failure Process in Tensile Components

The competing effects of failure by net section stress rupture and failure due to crack growth in creeping structural alloys have been investigated to determine the dominant failure process under various constant load service conditions. Two sets of experimental information were utilized: times to failure by quasi-homogeneous damage accumulation represented by Larson-Miller master curves, and creep crack growth rate information correlated either with C* for creep-ductile materials or with K for creep-brittle materials. A criterion, phrased in terms of the applied stress, temperature and initial crack length, has been established to justify the rate-determining fracture process. A number of materials, ranging from ductile materials such as Type 304 stainless steel, IN800H and low alloy steels obeying C*-controlled crack growth, to brittle materials such as Ni-based superalloys obeying K-controlled crack growth, have been studied. Both the configurations of infinite bodies and finitesize specimens were considered. The results show that for those materials where crack growth is C*-controlled, eventual failure is governed by quasi-homogeneous creep damage accumulation; whereas, for the materials with K-controlled crack growth, creep crack growth is likely to govern the final failure of engineering structures.

Influence of singularity dominated zone for propagating cracks in finite size specimens

The singularity dominated zones for straight as well as curved cracks propagating in finite size specimens were determined experimentally by using the optical method of dynamic photoelasticity using the near-field stress equations. Experimental data was carefully analyzed using improved numerical schemes to get the complete stress field around the propagating crack. This stress field was critically examined to evaluate the size of singularity dominated zones for cracks propagating in straight as well as curved paths. For this purpose, the exact solution was compared with the singular solution using stress components σ x, σ y, τ xy and the maximum shear stress τ max as a criterion respectively. For straight cracks where the stress field is symmetric about the crack path, the singularity dominated zones can be determined by using any one of the stresses. However, for a curved crack, the zones were unsymmetric. This study shows that σ y , the crack opening stress, yields the best result for characterizing the singularity dominated zone around a running crack tip.

Process zone analysis for the single-edge notched specimen: Part I. Process zone size and crack profile

A systematic analysis of the process zone is presented. Relations among the process zone size, load and crack opening displacement (COD) are derived using the weight function method and a power function closing pressure distribution in the process zone. These relations are specialized and used to study the behaviour of the single-edge notched (SEN) specimen loaded in tension and in bending. This study shows that the method presented here may be successfully used to analyze the fracture of finite-size specimens.

Probabilistic analysis of fatigue crack propagation in finite size specimens

By taking into account the effect due to the finiteness of the specimen's size, stochastic fatigue crack propagation processes are investigated on the basis of a Markov approximation method. Since the limiting property proved by Koiter causes a particular kind of singularity on the governing equation, the so-called death point must be introduced into the range of finite crack size. In the present study, the Fokker-Planck equation in a generalized sense is derived for such a particular case, and the influence of the specimen's size on the statistical properties of the residual life of the component is clarified by the use of numerical calculations.

Analytical study of J estimation formulas for three-point bend specimen.

Rice has shown a simplified method for estimating the J-integral of a deeply cracked bend bar, that is J==2U/Bb where U is the area under the load versus the load point displacement curve, B is the specimen thickness and b is the remaining ligament. It has not been made clear, however, how deep is a deep enough crack for finite size specimens. In this study, an applicable range of the Rice formula for the three-point bend specimen used in the elastic-plastic fracture toughness JIC test is studied analytically. The Rice formula is compared directly with the definition of J as a change in potential energy. Results show that an assumption of a deep crack is required only for a linear elastic material and is not required necessarily for a rigid perfectly-plastic material. In order to obtain the quantitative data, the conditional equation is calculated numerically by varying the crack length for three materials; linear elastic, rigid perfectly-plastic and elastic perfectly-plastic. Results show that the Rice formula is valid when a/W≳0.4 for a linear elastic material. Based on the results, a recommended precrack length of the three-point bend specimen in the JIC test is newly proposed.

Fracture of finite-sized specimens by wedge-shaped strikers : Bobryakov, AP Inst. Min, Novosibirsk, SU Dudolav, LS Inst. Min, Novosibirsk, SU Smirnov, VV Inst. Min, Novosibirsk, SU 2R. Sov. Min. Sci, V10, N6, Nov–Dec. 1974, P750–754

Fracture of finite-sized specimens by wedge-shaped strikers : Bobryakov, AP Inst. Min, Novosibirsk, SU Dudolav, LS Inst. Min, Novosibirsk, SU Smirnov, VV Inst. Min, Novosibirsk, SU 2R. Sov. Min. Sci, V10, N6, Nov–Dec. 1974, P750–754

Fracture of finite-sized specimens by wedge-shaped strikers

Fracture of finite-sized specimens by wedge-shaped strikers

Current noise in finite-sized specimens

The spatial correlation of generation-recombination noise in intrinsic germanium is investigated. In an analytical model the specimen is assumed to consist of mutually uncorrelated elements of resistance fluctuation. By comparison with measured values the size of the mutually uncorrelated elements is found to be approximately equal to four times the diffusion length of excess carriers in the semiconductor. A plausible explanation of the above results is indicated. Potential fluctuations at various terminals are calculated utilizing the analytical model and are found to agree with experimentally measured values. It is shown that the potential fluctuations at any pair of terminals is due to both the resistance fluctuations of individual elements and the associated current redistribution in the specimen. The latter gives rise to negative coefficients of spatial correlation which were experimentally verified.