Ductile tearing of pipeline-steel wide plates: II. Modeling of in-plane crack propagation

The purpose of this work is to develop a finite element simulation of static ductile tearing tests carried out on pipeline-steel wide plates. Experiments have been presented in a companion paper (Part I [1]).The simulation is based on an extension of the Gurson–Tvergaard–Needleman model which includes plastic anisotropy and viscoplasticity effects. The parameters of the model are fitted using tensile specimens (smooth and notched bars). Simulated tests are used to evaluate macroscopic fracture parameters which were experimentally measured: the energy dissipation rate R and the thickness reduction Z.The simulation tool is then used to numerically investigate the effect of plate thickness, plastic anisotropy and through-thickness hardness gradients on the crack growth resistance. It is shown that with increasing thickness, the energy dissipation rate first increases and then decreases. A through-thickness hardness gradient is beneficial when the surface is harder than the bulk. Plastic anisotropy can be either detrimental or beneficial depending on the loading direction. These effects are explained in terms of plastic localization inducing necking along the crack path and in terms of stress distribution.     

Ductile tearing in part-through cracks: experiments and cell-model predictions

This study describes an application of the computational cell model to predict ductile crack growth measured in experiments performed on surface-cracked, thick plates fabricated from a ferritic pressure vessel steel. The cell model limits void growth and coalescence to within a thin layer of material over the crack plane. Outside this layer, the material deforms plastically but remains void free. The Gurson–Tvergaard dilatant plasticity model describes the evolution of void growth and the associated macroscopic softening within the cells. Material-specific, cell parameters readily separate into two categories: those describing the micromechanics of void growth rate and those describing the local fracture process of the cell. Calibration of these parameters utilizes both discrete (3-D) cell models and R-curves measured using standard deep-notch bend or compact tension specimens. The cell model is applied here to surface-cracked plates subjected to different loading histories of tension and bending. The calibrated cell model reproduces accurately full details of the load-deformation records and the crack growth profiles for all the cases. These numerical studies suggest that the computational approach based on the cell model provides an engineering tool to predict ductile crack growth behavior in flawed structural components.     

Ductile tearing resistance of metal sheets

The concept of R-curves has been adopted to characterise stable crack extension and predict residual strength of thin-walled structures particularly in the aircraft industry. The present contribution uses results of FE simulations of crack extension in panels by the cohesive model to validate analytical procedures for determining J-integral values at large crack extension from measurable quantities, namely the force vs. displacement records. The numerically determined J-integral is taken as the benchmark for the outcome of the analytical formulas. The geometry dependence of J and CTOD based R-curves is investigated and alternative concepts like CTOA and dissipation rate at crack extension are discussed.     

Ductile tearing in thin aluminum panels: experiments and analyses using large-displacement, 3-D surface cohesive elements

This paper describes a large-displacement formulation for a 3-D, interface-cohesive finite element model and its application to predict ductile tearing in thin aluminum panels. A nonlinear traction-separation relationship defines the constitutive response of the initially zero thickness interface elements. Applications of the model simulate crack extension in C(T) and M(T) panels made of a 2.3 mm thick, Al 2024-T3 alloy tested as part of the NASA-Langley Aging Aircraft program. Tests of the M(T) specimens without guide plates exhibit significant out-of-plane (buckling) displacements during crack growth which necessitates the large-displacement, cohesive formulation. The measured load vs. outside surface crack extension behavior of high constraint (T-stress>0) C(T) specimen drives the calibration process of the cohesive fracture model. Analyses of low constraint M(T) specimens, having widths of 300 and 600 mm and various a/W ratios, demonstrate the capabilities of the calibrated model to predict measured loads and measured outside surface crack extensions. The models capture accurately the strong 3-D effects leading to out-of-plane buckling and various degrees of crack front tunneling in the C(T) and M(T) specimens. Previous analyses of these specimens using a crack tip opening angle (CTOA) criterion for growth show good agreement with measured peak loads. However, without the ability of the interface-cohesive model to predict tunneling behavior, the CTOA approach overestimates crack extensions early in the loading when tunneling behavior dominates the response.     

Deformation and tearing of blast-loaded stiffened square plates

Experimental and numerical results for fully built-in stiffened square plates subjected to blast pressure loading are presented. The strain rate-sensitive plates exhibit mode I (large ductile deformation) and mode II (tensile tearing) failure as the load intensity increases. The numerical analysis is carried out using a finite element formulation which incorporates non-linear geometry and material effects as well as strain rate sensitivity. Mode I is predicted well for both maximum deflection and deformation shape. Initiation of mode II failure is predicted by a maximum strain criterion, but the limited mode II data is insufficient for conformation.     

Ductile tearing assessment of high-strength steel X-joints under in-plane bending

This study reports an experimental investigation of a fatigue-cracked, pre-notched circular hollow section X-joints fabricated from high strength steels (with the yield strength higher than 800 MPa) subjected to brace in-plane bending. The circular hollow section X-joint entails a prefabricated V-notch near the weld toe at the crown position. The experimental procedure applies a fatigue pre-cracking cyclic load followed by a monotonic brace in-plane bending, which leads to brittle through-thickness crack propagation after some amount of ductile tearing. The ductile tearing assessment, integrating the fracture resistance curve obtained from the small-scale fracture specimens and the crack extension in the large-scale tubular joint, predicts closely the load level at which unstable crack extension takes place. The generic level 2A curve outlined in the BS7910 provides an un-conservative estimate on the failure load of the X-joint specimen. The parametric numerical investigation reveals that the strength definition for the cracked joints imposes a significant effect on the shape of the failure assessment curve.     

Dynamic viscosity of gases over a wide range of temperatures. I

The results are presented of a generalization of the experimental data on the viscosities of He, Ne, Ar, Kr, Xe, and N₂ at atmospheric pressure over the range of temperatures from the boiling point at atmospheric pressure to 2000 K using polynomial approximating relationships.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 56, No. 6, pp. 982–987, June, 1989.     

Size effects in the axial tearing of circular tubes during quasi-static and impact loadings

An experimental investigation is reported into the size effect for thin-walled mild steel circular tubes which are axially split and then plastically rolled up on a conical mandrel when their upper ends were pressed by the cross-head of a testing machine or struck by a heavy mass with impact velocities of 9.0 and 13.5 m/s. The test tubes have scale factors of one, two and four. Deviations of 11–57 percent from the elementary geometrically similar scaling laws are observed in the maximum permanent axial deflection, u_max, tearing length, Δa, diameter of plastically deformed curls, d, specific energy absorbed, w, and average axial force, F_ave. The material strain rate hardening effect is the main factor causing these deviations. A new scaling law including material strain rate hardening effect is suggested.     

Dynamic vs. quasi-static shear failure of high strength metallic alloys: Experimental issues

Ductile fracture of metals by void nucleation, growth and coalescence under positive stress triaxiality is well admitted. This is not the case when metals are submitted to negative stress triaxiality. The present work aims at contributing to a better understanding of the competition between micro-mechanisms at the origin of failure of metals when submitted to shear-pressure loading at low and high strain rates. With this aim in view, experiments were carried out on Ti–6Al–4V shear-compression samples involving a stress triaxiality range comprised between −0.2 and −0.5. Results show that the material failure is the consequence of a void growth induced process. At high strain rate, due to the localization of the deformation within adiabatic shear bands, the failure of the material occurs earlier, leading to maximum shear strain smaller at high strain rate than at low strain rate. Impact tests were also carried out on Kalthoff and Winkler type double notched plates. They showed that the interaction between tension and shear waves leads to a complex Mode I–Mode II crack propagation.     

The re-characterisation of complex defects: Part I: Fatigue and ductile tearing

Defect assessment codes idealise complex defects as simple shapes which are amenable to analysis in a process known as re-characterisation. The present work examines the re-characterisation of complex defects which extend by fatigue, ductile tearing or cleavage. A family of representative defects were analysed numerically, while a related experimental programme investigated defect interaction and failure. Part I of the paper focuses on fatigue and ductile tearing. Part II examines cleavage. The numerical and experimental results are discussed within the context of the re-characterisation procedures described in BS 7910 (Guidance on methods for assessing the acceptability of flaws in metallic structures. London, UK: British Standard Institution; 1999 [Chapter 7]) and R6/4 (Assessment of the integrity of structures containing defects. Gloucester: British Energy Generation Ltd.; 2001 [Revision 4, Chapters I and II.3]).The level of conservatism of the re-characterisation procedures for fatigue and ductile tearing are discussed. A possible non-conservatism of the re-characterisation for cleavage is discussed in Part II, within the framework of constraint based statistical fracture mechanics.     

Three-dimensional finite element simulations of mixed-mode stable tearing crack growth experiments

Mixed-mode stable tearing crack growth events in Arcan plate specimens made of aluminum alloy 2024-T3 are simulated using three-dimensional (3D) finite element methods. A modeling/simulation procedure utilizing a mixed-mode CTOD fracture criterion and the custom 3D crack growth simulation software, CRACK3D, with an automatic local re-meshing option is demonstrated. Simulation predictions of the load-crack extension curve and the in-plane curvilinear crack growth path are compared with experimental measurements for various mixed-mode loading cases. Issues such as the effects of near-tip finite element size and crack extension increment size on simulation predictions are investigated.     

Thermomechanical response of HSLA-65 steel plates: experiments and modeling

To understand and model the thermomechanical response of high-strength low-alloy steel (HSLA-65), uniaxial compression tests are performed on cylindrical samples, using an Instron servohydraulic testing machine and UCSD’s enhanced Hopkinson technique. True strains exceeding 60% are achieved in these tests, over the range of strain rates from 10⁻³/s to about 8500/s, and at initial temperatures from 77 to 1000 K. The microstructure of the undeformed and deformed samples is examined through optical microscopy.The experimental results show: (1) HSLA-65 steel displays good ductility and plasticity (strain > 60%) even at low temperatures (even at 77 K) and high strain rates; (2) at relatively high temperatures and low strain rates (especially below about 0.1/s), its strength is temperature-insensitive, indicating that the material has good high-temperature weldability; (3) slight dynamic strain aging (DSA) occurs at temperatures over 400 K and in the range of strain rates from 0.001/s to 3000/s, the maximum values of the stress shifting to higher temperatures with increasing strain rates; and (4) the microstructure of the material is not affected much by the changes in the strain rate and temperature.Finally, based on the mechanism of dislocation motion, and using our experimental data, the parameters of a physically-based model developed earlier for AL-6XN stainless steel [J. Mech. Phys. Solids 49 (2001) 1823] are estimated and the model predictions are compared with various experimental results, excluding the dynamic strain aging effects. Good agreement between the theoretical predictions and experimental results is obtained. In order to further verify the model independently of the experiments used for the evaluation of the model parameters, additional compression tests at a strain rate of 8500/s and various initial temperatures are performed, and the results are compared with the model predictions. Good correlation is observed. As an alternative to this model, the experimental data are also used to estimate the parameters in the Johnson–Cook model [Proceedings of the Seventh International Symposium on Ballistics, The Hague, The Netherlands, p. 541] and the resulting model predictions are compared with the experimental data, again excluding the dynamic strain-aging effects. These and related results suggest that the physically-based model has a better prediction capability over a broader strain rate and temperature range.     

Deformation and tearing of circular plates with varying support conditions under uniform impulsive loads

Transient dynamic finite element analysis of circular plates with varying support configurations under uniform single square wave form impulsive load has been carried out in FEA package ANSYS. Experimental results of Teeling-Smith and Nurick [The deformation and tearing of thin circular plates subjected to impulsive loads. Int J Impact Eng 1991;11(1):77–91] and Nurick et al. [Tearing of blast loaded plates with clamped boundary conditions. Int J Impact Eng 1996;18(7–8):803–27] for the onset of thinning and tearing at the boundary of clamped circular plates subjected to uniformly loaded air blasts have been used to compare and validate the numerical simulation and procedure. The Mode II failure with respect to clamped circular plates has been simulated using a rupture strain criteria. Mode III failure or plastic shear sliding, has been considered using a shear strain failure criteria as proposed by Wen and Jones for plates. A stiffness reduction scheme has been proposed to decide on the initiation and progression of tearing in conjunction with suitable failure model under Modes II and III. The evolution of deflections, plastic zones, rupture zones and failure modes under the blast loading conditions are found to match well with the experimental results. The validated numerical model has further been used to study the effect of plate thickness on the deformation and tearing response of the circular plates subjected to impulsive loads. The deformation, tearing and shock absorption response of clamped circular plates under uniform impulsive loads with ring support of varying edge configurations at the boundary have also been numerically studied. Further, the response of circular plate–tube combination with varying boundary support configurations has been studied. The plate has been considered at the mid-span of the tube of length equal to the plate diameter with the ends of the tube modelled as clamped. The numerical model has been used to study the effect of tube thickness variations on the deformation and tearing response of the circular plate under shock loads. The response of tube–plate combinations under uniform impulsive loads with ring support at the plate–tube junction have also been numerically studied.     

Mechanical behavior and failure modes of aluminum/bamboo sandwich plates under quasi-static loading

Experimental investigations have been made on the quasi-static mechanical behavior and failure modes of aluminum/bamboo sandwich plates. Thermosetting epoxy resin and thermoplastic Polybond resin were used to bond the aluminum sheets and the bamboo. Tensile, compressive and flexural properties were evaluated. The effects of bond conditions on the mechanical behavior and failure modes were examined. The thermoplastic Polybond resin resulted in a stronger interface bond than the thermosetting epoxy resin. The improvement of the interface bond led to significant increases in compressive and flexural properties. The tensile properties were found to be insensitive to the interface bond. The dominant failure mechanisms affected by the interface bond dictated the mechanical properties of the sandwich plates in individual loading conditions.     

Ductile tearing simulation of Battelle pipe test using simplified stress‐modified fracture strain concept

In this paper, numerical ductile tearing simulation results are compared with six circumferential through‐wall and surface cracked pipes made of two materials (SA‐333 Gr. 6 and A106 Gr. B carbon steels), performed at Battelle. For simulation, a model using a simplified fracture strain model is employed, by analysing tensile data of the material. By comparing experimental J‐R data with FE simulation results, the damage model dependent on the element size is determined based on the ductility exhaustion concept. The model is used to simulate ductile tearing behaviour of six circumferential through‐wall and surface cracked pipes. In all cases, simulated results agree well with experimental load, crack length and crack mouth opening displacement versus load line displacement data.     

Dynamic in-plane resonant characteristics of piezoceramic and piezolaminated composite plates.

Piezolaminated composite plates have received considerable attention in various industrial applications due to their intelligent characteristics. In this investigation, two experimental measurement techniques are used to determine the in-plane resonant vibration of angle-ply laminated composites embedded with a piezoceramic layer (piezolaminated plates) for different stacking angles. The first method is a full-field optical technique, which is called the AF-ESPI (amplitude-fluctuation electronic speckle pattern interferometry). This is the major experimental method. The AF-ESPI method is used to determine the in-plane resonant frequency and corresponding mode shape of a single-layer piezoceramic plate and piezolaminated plates with five different stacking angles. The second experimental technique, the impedance analyzer, is employed to determine the in-plane resonant frequency. Finally, numerical computations based on the finite element analysis are presented for comparison of the two experimental results. Excellent agreement between the experimentally measured data and the numerically calculated results are found for in-plane resonant frequencies and mode shapes. This study indicates that the dynamic characteristics of inplane resonant vibrations for piezolaminated plates with different stacking angles are quite different.     

Dynamic stability of viscoelastic plates

The problem of dynamic stability of viscoelastic plates with any kernel of relaxation is reduced to the investigation of stability of the trivial solutions of a set of ordinary integro-differential equations with periodic coefficients. Using the Laplace integral transform, an integro-differential equation is reduced again to the integro-differential equation of which the main part coincides with the damped Hill equation. Changing this equation for the system of two linear equations of the first-order and using the averaging method, the monodromy matrix of the obtained system is constructed. Considering the absolute value of the eigenvalues of monodromy matrix is greater than unit, the condition for instability of trivial solution is obtained in the three-dimensional space of parameters corresponding to the frequency, viscosity and amplitude of external action. Analysis of form and size of instability domains is carried out.     

Damage assessment of thin SiC/SiC composite plates subjected to quasi-static indentation loading

Tri-dimensional woven SiC/SiC composite was subjected to quasi-static indentation tests at room temperature. For this purpose, hemispherical indentors and circular supports of various diameters were used. The extent of damage was evaluated with the help of optical and scanning electron microscopy. Formation of cone cracks initiating from the indented site is observed. The predominant internal damages (fibre bundle and matrix cracking) remain localised beneath the indentor. The indented specimens were tensile tested at room temperature to determine their residual strength. Results indicate that the strength reduction is proportional to the diameter of the damaged zone evaluated on the back side of the specimen.