Fixed Grip Condition Research Articles

A numerical study on the correlation of ductile crack extension in Ni-based clad pipe girth welds with circumferential surface cracks and clamped SE(T) specimens

This work describes a numerical investigation on the relationships between ductile crack extension in Ni-based clad pipe girth welds and an API X80 pipeline steel with circumferential surface cracks and SE(T) specimens under fixed grip conditions. A primary objective is to gain further insight and understanding of the effects of constraint on ductile tearing behavior in piping components with dissimilar girth welds and how well crack growth resistance curves measured using single edge notched tension fracture specimens correlate with ductile fracture behavior in circumferentially surface cracked pipes. The numerical description of CTOD−R curves employs a computational cell approach incorporating the Gurson–Tvergaard (GT) constitutive model to simulate ductile crack extension in the crack configurations analyzed. The numerical analyses consider predictions of ductile crack growth in 3-D models of circumferentially cracked pipes with varying crack depth over pipe thickness ratio, a/t, from measured J-resistance curves derived from fracture resistance testing of clamped SE(T) specimens. The analyses also focus on comparing predictions of ductile crack extension using two different definitions for the CTOD.

Phase field crystal study of nano-crack growth and branch in materials

The phase field crystal (PFC) method is a new multiscale method, which can reproduce physical phenomena on an atomic level and on a diffusion time scale for the microstructure evolution of materials. The morphology of microcrack propagation and the branch of single crystal materials under tensile strain with a fixed grip condition are simulated by using PFC coupling with an external field method. The results show that microcrack propagation depends a lot on the applied strain. The crack starts to grow and branch when the strain reaches a critical value for biaxial tension. The temperature parameter may also have an effect on crack propagation and the branch. In order to indicate the connection between the PFC results and materials behavior, the energy balance approach is used to analyze the mechanism of crack extension, and also the critical value of the strain for crack extension is obtained. The simulated results are in good agreement with other simulation results and experimental results.

FGM Gradation Direction Effects on Mixed-Mode Crack Initiation Angle by MLPG Method

In this article, the meshless local Petrov–Galerkin method is used to analyze the cracked plate made of functionally graded material. The stress intensity factor of Mode I & II, maximum energy release rate and crack initiation angle are determined under the influence of various nonhomogeneity ratios, crack length, and material gradation angle. To solve discrete dynamic equations, a new effective method is extended and utilized. To find crack initiation angle, a simple and easy to use formula is suggested here. The edge-cracked functionally graded plate is considered under the uniform membrane and fixed grip conditions; also, the center-cracked functionally graded plate is analyzed under the uniform membrane and impact loads.

Fractal materials, beams, and fracture mechanics

Continuing in the vein of a recently developed generalization of continuum thermomechanics, in this paper we extend fracture mechanics and beam mechanics to materials described by fractional integrals involving D, d and R. By introducing a product measure instead of a Riesz measure, so as to ensure that the mechanical approach to continuum mechanics is consistent with the energetic approach, specific forms of continuum-type equations are derived. On this basis we study the energy aspects of fracture and, as an example, a Timoshenko beam made of a fractal material; the local form of elastodynamic equations of that beam is derived. In particular, we review the crack driving force G stemming from the Griffith fracture criterion in fractal media, considering either dead-load or fixed-grip conditions and the effects of ensemble averaging over random fractal materials.

A macroscopic-level hybrid lattice particle modeling of mode-I crack propagation in inelastic materials with varying ductility

This paper presents a numerical method, known as hybrid lattice particle modeling (HLPM), for the study of mode-I crack formation and propagation in two-dimensional geometry subject to a fixed-grip condition. The HLPM combines the strength of two numerical techniques, particle model (PM) and lattice model (LM), for the purpose of solving dynamic fragmentation of solids within a various Poisson’s ratio range. A Lennard-Jones-type potential is employed to describe the nonlinear dynamic interaction of each macroscopic-size particle with its nearest-neighbors. Crack initiation and propagation is investigated for materials with different Young’s modulus, tensile strength and varying ductility. It is demonstrated that crack patterns and propagation closely match the anticipated physical behavior of inelastic materials. Finally, the HLPM is applied to the investigation of a functionally designed composite material of an elastic–brittle infrastructure material coated with a ductile layer for the protection of fracture propagation. The ultimate application is aimed at the retrofitting of failing infrastructure.

The Bridged Crack Model for the Analysis of Brittle Matrix Fibrous Composites Under Repeated Bending Loading

In this paper, we present a fracture-mechanics based model, the so-called bridged crack model (Carpinteri, A., 1981, “A Fracture Mechanics Model for Reinforced Concrete Collapse,” Proc. of IABSE Colloquium on Advanced Mechanics of Reinforced Concrete, Delft, I.A.B.S.E., Zürich, pp. 17–30; Carpinteri, A., 1984, “Stability of Fracturing Process in R.C. Beams,” J. Struct. Engng. (A.S.C.E.), 110, pp. 544–558) for the analysis of brittle matrix composites with discontinuous ductile reinforcements under the condition of repeated bending loading. In particular, we address the case of composites with very high number of reinforcements (i.e., fiber-reinforced composites, rather than conventionally reinforced concrete). With this aim, we propose a new iterative procedure and compare it to the algorithm recently proposed by Carpinteri, Spagnoli, and Vantadori (2004, “A Fracture Mechanics Model for a Composite Beam with Multiple Reinforcements Under Cyclic Bending,” Int. J. Solids Struct., 41, pp. 5499–5515), showing the advantages in terms of computational efficiency. Furthermore, we analyze the combined effects of crack length, brittleness number, and fiber number on the cyclic behavior of the composite beam, showing the conditions enhancing the energy dissipation in the composite system. Eventually, we analyze crack propagation and propose, consistently with the model premises, a fracture-mechanics-based crack propagation criterion that allows one to simulate cyclic bending tests under the fixed grip condition.

A Tensile-Load Relaxation Test for Measuring the Stress Enhanced Corrosion Exponent of Ceramics with Open Porosity

A tensile test is proposed for evaluating the stress enhanced corrosion-coefficient of ceramics with open porosity. The analysis of load at fixed grip conditions bases on the assumption that stress corrosion results in a spread of pre-existing generalised damage seen as micro-crack starter due to open porosity. Sub-critical crack extension of microcracks departs from pores and provokes a time dependant diminution of the Young’s modulus, and of the stiffness, of the tested sample. The description derives the number and the size of pre-existing micro-cracks with respect to time. The density of microcrack-nuclei results from the process and belongs to the microstructure, i.e., the number of channels or crack starters, and is considered to remain constant. The rate of diminution of the load is considered, either with respect to the initial one or to a deduced stress intensity factor. Simple relationships yield then an approximate diagram for stress enhanced corrosion. Samples resulting from sintering a mixture of alumina and titania powders were tested under tempered water flow. A stress corrosion exponent, n = 16, near to that of alumina was obtained.

135 貫通き裂を有する傾斜機能圧電セラミックス厚板の電気熱弾性相互干渉(OS1-8 先端・機能材料の破壊現象(1),OS1 先端・機能材料のマルチスケール解析3)

In this study the theoretical analysis of a thermoelectroelasticity problem is developed for a piezoelectric plate due to thermal loading under a uniform electric field and a fixed grip condition. The plate is a functionally graded material, meaning that its thermo-electro-mechanical properties are assumed to be continuous functions of the thickness coordinate. The plate contains an embedded or an edge crack perpendicular to its boundaries. The Fourier transform technique is used to formulate the problem in terms of a singular integral equation. The singular integral equation is solved by using the Gauss-Jacobi integration formula. Numerical calculations are carried out, and the mode I stress intensity factors and energy density factors are presented for embedded as well as edge crack for various values of dimensionless parameters representing the size and location of the crack, the material nonhomogeneity, the surface temperatures and the loading combinations.

Fracture of Brittle Microbeams

The random polycrystalline microstructure of microbeams necessitates a reexamination of the crack driving force G stemming from the Griffith fracture criterion. It is found that, in the case of dead-load conditions, G computed by straightforward averaging of the spatially random elastic modulus E is lower than that obtained by correct ensemble averaging of the stored elastic energy. This result holds for both Euler-Bernoulli and Timoshenko models of micro-beams. However, under fixed-grip conditions G is to be computed by a direct ensemble averaging of E. It turns out that these two cases provide bounds on G under mixed loading. Furthermore, crack stability is shown to involve a stochastic competition between potential and surface energies, whose weak randomness leads to a relatively stronger randomness of the critical crack length.

THERMALLY INDUCED FRACTURE OF A FUNCTIONALLY GRADED PIEZOELECTRIC LAYER

The theoretical analysis of a thermoelectroelasticity problem is developed for a piezoelectric layer due to a thermal load under a uniform electric field and a fixed grip condition. The layer is assumed to be a functionally graded material, meaning that its thermoelectromechanical properties are assumed to be continuous functions of the thickness coordinate. The layer contains an embedded or an edge crack perpendicular to its boundaries. The Fourier transform technique is used to formulate the problem in terms of a singular integral equation. The singular integral equation is solved by using the Gauss–Jacobi integration formula. Numerical calculations are carried out, and the mode I energy density factors are presented for embedded as well as edge cracks for various values of dimensionless parameters representing the size and the location of the crack, the material nonhomogeneity, the surface temperatures, and the loading combinations.

Birdcaging and the collapse of rods and cables in fixed-grip compression

Wound cables and straight rods exhibit lateral instabilities when loaded under compression and rotation in fixed-grip conditions. In a multi-strand cable made from helically wound strands, this produces a “bird cage” structure where the constituent strands separate to leave a central void region. For a straight rod, a similar instability occurs when the planar elastica becomes unstable under significant axial compression. The large deflection theory of linear elastic rods is used to explain these behaviours in terms of the standard concepts of the theory of buckling, post-buckling, and imperfection sensitivity. The problem provides an excellent vehicle for the use of Euler parameters (quaternions) which remove the singularities normally associated with an Euler angle formulation.

Periodic cracking of elastic coatings

In this study the periodic cracking of an elastic coating bonded to a homogeneous substrate is considered. The problem is assumed to simulate the segmentation or “mud-flat” cracking of ceramic layers used as thermal barrier coatings in stationary and aircraft gas turbine engines. By expressing the displacements in terms of a combination of finite and infinite Fourier transforms, the corresponding mixed boundary value problem is reduced to an integral equation with the crack surface displacement as the unknown function. The main objective of the study is the examination of the influence of the length parameters c/b and b/h and the stiffness ratio μ2/μ1 on the crack tip stress intensity factors, the crack opening displacement, the strain energy released as a result of periodic cracking, and the in-plane tensile stress on the coating surface, where c, b, h, μ1 and μ2, respectively, are crack spacing, crack depth, coating thickness, shear modulus of the coating, and shear modulus of the substrate. The case of a periodically cracked strip is investigated separately and the stress intensity factors under fixed-load and fixed-grip conditions are compared. Also, the validity of the assumption made in simple energy balance calculations to the effect that the entire strain energy contained within the volume of the cell is released during periodic cracking is studied. It is shown that such an assumption is valid only for very small values of relative crack spacing c/b.

An investigation of a dynamic crack propagation in a two-dimensional viscoelastic solid

The dynamic crack propagation in a two-dimensional viscoelastic solid is studied by using finite element method to model the specimen and modal analysis to obtain the solution of the equations of motion. As a fracture criterion it is assumed that the crack propagates with a constant velocity so that the energy release rate is determined as a function of the variable crack length for a given fixed load or fixed grip condition. It is proven numerically that the local energy release rate equals the global energy release rate which states the energy conservation law and shows the validity of the applied method.

Effect of geometry and poisson ratio on stress-intensity factors in a sen specimen under fixed-grip conditions

A finite-element analysis is performed to evaluate the influence of the geometrical configuration and of Poisson's ratio on the stress-intensity factor (SIF) prevailing in a single-edge-notch specimen (SEN) under fixed-grip conditions. It is found that the shorter the specimen and the longer the relative crack length, the greater the effect of geometry becomes. Moreover, even for very long specimens the SIF increasingly deviates from its value in a SEN specimen under uniform tensile stress as the crack length increases. Under constant remote displacement a variation in Poisson's ratio in the range of 0–0.5 results in a considerable increase of up to 33% in the SIF, for short specimens and long crack length, whereas, if under similar boundary conditions the remote applied load to the specimen is maintained constant, an increase in Poisson's ratio results in a sharp decrease in the SIF for short specimens and short crack length.

The Crack-Arrest Properties of 9%Ni Steel and its Weldment (1st Report)

In the previous papers, the authors proposed a realistic crack arrest concept to assess the structural integrity of LNG storage tank and the surface-notched double tension test to evaluate the crack arrest properties of 9% Ni steels and their weldments. This paper deals with dynamic analysis of the run/arrest events confirmed in the surface-notched double tension tests conducted on 9% Ni steels by three-dimensional linear elastic finite element method.Prior to the analysis, dynamic deformation behaviors of the specimen and crack velocities were measured under the potentially extensive propagation and arrest of brittle crack during testing. These experiments verified that a brittle crack propagated through the specimen and/ or was arrested at the notch tip under the fixed grip conditions. These experimental data were used as input data in the analysis by general purpose program ADINA. Crack propagation was simulated in such manners that the nodal points on crack propagation line were constrained by truss elements which were eliminated at the time interval corresponding to crack velocity. Excellent agreement was obtained between experimental and FEM results as to the dynamic deformation behavior of specimen. Variation of dynamic stress intensity factor with crack propagation was obtained by energy balance theory.Dynamic analysis shows that KD decreases as the notch depth becomes shallow and that KD indicates minimum value at the notch end. In linear elastic fracture mechanics, the arrest of propagating crack is to occur when dynamic stress intensity factor KD of the crack becomes lower than crack arrest toughness Ka of the material. Present results of experiments and analyses do not necessarily support the Ka concept stated above because it happened that KD of the propagationg crack showed lower value than that of the arrested crack.Crack arrest at the notch end occurs if sufficient plastic deformation is allowed there when triaxiality at the crack tip is low and crack velocity is slower than plastic wave velocity. Since the surface defects existed in the welded structure are generally small, there hardly exists the possibility of crack propagation failure of 9% Ni steel and its weldment in LNG storage tank.

Stability of circumferential through-cracks in ductile pipes

An analysis of tearing instability is presented for a pipe with a circumferential through-crack. Loading conditions consisting of a large external axial force and a bending moment, together with an internal pressure, have been considered. The mechanical behavior of the material is assumed to be elastic perfectly-plastic. Instability has been studied under fixed grip conditions, following the application of loads which correspond to the plastic limit load of the cracked cross-section. The values of the applied tearing modulus have been expressed in terms of geometrical factors such as pipe length, pipe radius, and the length of the crack. Numerical examples have been calculated to obtain an estimate of the critical value of the length-to-radius ratio, for the case that the tearing modulus of the material is known.

Unstable fracture from stable fibrous crack growt

A criterion of the transition from stable fibrous crack growth to unstable fracture is investigated on the basis of J-integral R curve concept.The slope of JR curve is compared with that of crack driving force curve under fixed grip condition. Instability condition is expressed bydJR/da≤dJF.G./daAnd the expression of above formula for bending specimen is obtained which is a general form of the expression after Paris et al.Three-point bending tests with spring bars were carried out at temperatures above brittle-ductile transition. Instability occurred after stable fibrous crack growth at the lower level of J value than conventional bending tests.The proposed instability criterion compares well with the test results.

Further Dynamic Finite Element Analysis of the Tapered DCB Specimen

A dynamic finite element code was used to compute the dynamic stress intensity factors and crack arrest stress intensity factor which are related to the crack run-arrest response in a tapered double cantilever beam (DCB) specimen machined from A533B steel. Measured crack velocities of a fracturing tapered DCB specimen were used to prescribe a crack motion under both fixed grip and variable loading conditions at the two loading pins. Numerically and experimentally determined dynamic strains were compared at three locations on the fracturing tapered DCB specimen. This comparative study showed that the fixed grip condition modeled the actual dynamic state well and that the crack arrest stress intensity factor, KIa, computed on the bases of fixed grip and variable loading conditions differed by a factor of approximately 0.6.

The influence of non-fracturing reinforcing elements on crack propagation in metal sheets

Studies have been made of crack propagation in fibre-reinforced metal sheets. The reinforcing fibres were arranged not to fracture, whatever the tensile extension of the composite structure by use of a controlled decoupling mechanism, acting at the fibre/sheet interface. The fibres carry loads across the entire length of a crack in the sheet and energy is absorbed by interactions between the components of the composite structure as the crack extends. Two conditions for crack growth have been investigated: (a) an edge crack with non-uniform loading conditions, and (b) a central crack with uniform tensile loading of sheet under fixed-grip conditions.

An investigation of propagating cracks by dynamic photoelasticity

A 16-spark gap, modified schardin-type camera was constructed for use in dynamic photoelastic analysis of fracturing plastic plates. Using this camera system, dynamic photoelastic patterns in fracturing Homalite-100 plates, 3/8 in. × 10 in. × 15 in. with an effective test area of 10 in. × 10 in., loaded under fixed grip condition were recorded. The loading conditions were adjusted such that crack acceleration, branching, constant velocity, deceleration and arrest were achieved.