Significant issues in proof testing: A critical appraisal

Issues which impact on the interpretation and quantification of proof test benefits are reviewed. The importance of each issue in contributing to the extra quality assurance conferred by proof testing components is discussed, particularly with respect to the application of advanced fracture mechanics concepts to enhance the flaw screening capability of a proof test analysis. Items covered include the role in proof testing of elastic-plastic fracture mechanics, ductile instability analysis, deterministic versus probabilistic analysis, single versus multiple cycle proof testing, and non-destructive examination (NDE). The effects of proof testing on subsequent service life are reviewed, particularly with regard to stress redistribution and changes in fracture behavior resulting from the overload. The importance of proof test conditions are also addressed, covering aspects related to test temperature, simulation of service environments, test media and the application of real-time NDE. The role of each issue in a proof test methodology is assessed with respect to its ability to: promote proof test practice to a state-of-the-art; aid optimization of proof test design; and increase awareness and understanding of outstanding issues

A Comparison of Single-Cycle Versus Multiple-Cycle Proof Testing Strategies

Single-cycle and multiple-cycle proof testing (SCPT and MCPT) strategies for reusable aerospace propulsion system components are critically evaluated and compared from a rigorous elastic-plastic fracture mechanics perspective. Earlier MCPT studies are briefly reviewed. New J-integral estimation methods for semi-elliptical surface cracks and cracks at notches are derived and validated. Engineering methods are developed to characterize crack growth rates during elastic-plastic fatigue crack growth (FCG) and the tear-fatigue interaction near instability. Surface crack growth experiments are conducted with Inconel 718 to characterize tearing resistance, FCG under small-scale yielding and elastic-plastic conditions, and crack growth during simulated MCPT. Fractography and acoustic emission studies provide additional insight. The relative merits of SCPT and MCPT are directly compared using a probabilistic analysis linked with an elastic-plastic crack growth computer code. The conditional probability of failure in service is computed for a population of components that have survived a previous proof test, based on an assumed distribution of initial crack depths. Parameter studies investigate the influence of proof factor, tearing resistance, crack shape, initial crack depth distribution, and notches on the MCPT vs. SCPT comparison. The parameter studies provide a rational basis to formulate conclusions about the relative advantages and disadvantages of SCPT and MCPT. Practical engineering guidelines are proposed to help select the optimum proof test protocol in a given application

A Comparison of Single-Cycle Versus Multiple-Cycle Proof Testing Strategies

Single-cycle and multiple-cycle proof testing (SCPT and MCPT) strategies for reusable aerospace propulsion system components are critically evaluated and compared from a rigorous elastic-plastic fracture mechanics perspective. Earlier MCPT studies are briefly reviewed. New J-integral estimation methods for semielliptical surface cracks and cracks at notches are derived and validated. Engineering methods are developed to characterize crack growth rates during elastic-plastic fatigue crack growth (FCG) and the tear-fatigue interaction near instability. Surface crack growth experiments are conducted with Inconel 718 to characterize tearing resistance, FCG under small-scale yielding and elastic-plastic conditions, and crack growth during simulated MCPT. Fractography and acoustic emission studies provide additional insight. The relative merits of SCPT and MCPT are directly compared using a probabilistic analysis linked with an elastic-plastic crack growth computer code. The conditional probability of failure in service is computed for a population of components that have survived a previous proof test, based on an assumed distribution of initial crack depths. Parameter studies investigate the influence of proof factor, tearing resistance, crack shape, initial crack depth distribution, and notches on the MCPT versus SCPT comparison. The parameter studies provide a rational basis to formulate conclusions about the relative advantages and disadvantages of SCPT and MCPT. Practical engineering guidelines are proposed to help select the optimum proof test protocol in a given application

A Comparison of Single-Cycle Versus Multiple-Cycle Proof Testing Strategies

Single-cycle and multiple-cycle proof testing (SCPT and MCPT) strategies for reusable aerospace propulsion system components are critically evaluated and compared from a rigorous elastic-plastic fracture mechanics perspective. Earlier MCPT studies are briefly reviewed. New J-integral estimation methods for semi-elliptical surface cracks and cracks at notches are derived and validated. Engineering methods are developed to characterize crack growth rates during elastic-plastic fatigue crack growth (FCG) and the tear-fatigue interaction near instability. Surface crack growth experiments are conducted with Inconel 718 to characterize tearing resistance, FCG under small-scale yielding and elastic-plastic conditions, and crack growth during simulated MCPT. Fractography and acoustic emission studies provide additional insight. The relative merits of SCPT and MCPT are directly compared using a probabilistic analysis linked with an elastic-plastic crack growth computer code. The conditional probability of failure in service is computed for a population of components that have survived a previous proof test, based on an assumed distribution of initial crack depths. Parameter studies investigate the influence of proof factor, tearing resistance, crack shape, initial crack depth distribution, and notches on the MCPT vs. SCPT comparison. The parameter studies provide a rational basis to formulate conclusions about the relative advantages and disadvantages of SCPT and MCPT. Practical engineering guidelines are proposed to help select the optimum proof test protocol in a given application

A Simplified SSY Estimate Method to Determine EPFM Constraint Parameter for Sensor Design

To implement a sensor structure analysis and design (as well as other engineering applications), a two-parameter approach using elastic⁻plastic fracture mechanics (EPFM) could be applied to analyze a structure more accurately than a one-parameter approach, especially for structures with low crack constraint. The application of the J-A two-parameter approach on sensors and other structures depends on the obtainment of a constraint parameter A. To conveniently and effectively obtain the A parameter values, the authors have developed a T-stress-based estimate method under a small-scale yielding (SSY) condition. Under a uniaxial external loading condition, a simplified format of the T-stress-based estimate has been proposed by the authors to obtain the parameter A much more conveniently and effectively. Generally, sensors and other practical engineering structures endure biaxial external loading instead of the uniaxial one. In the current work, the simplified formation of the estimate method is extended to a biaxial loading condition. By comparing the estimated A parameter values with their numerical solutions from a finite element analysis (FEA) results, the extension of the simplified formation of T-stress-based estimate method to biaxial loading was discussed and validated. The comparison procedure was completed using a wide variety of materials and geometrical properties on three types of specimens: single edge cracked plate (SECP), center cracked plate (CCP), and double edge cracked plate (DECP)

Numerical modelling of adhesive joints debonding under fatigue loading

Composite and hybrid metal/composite structures are nowadays present not only in the aerospace industry, but thanks to continuous performance improvement and cost reduction, also many more industrial fields are approaching the use of multimaterial structural elements. This requires, in turn, extensive use of adhesive bonding and a more and more sophisticated capability to simulate and predict the strength of bonded connections where, for this purpose, analytical methods are being progressively integrated or replaced by finite element analysis (FEA). To ensure the safety of the resulting structures, it is imperative to understand their fatigue behaviour. Thus the rise of the application of adhesive bonding has gone hand in hand with the development of models capable to predict the fatigue life that is related to the initiation and propagation of defects starting at free edges of joining regions or other features, such as throughthickness holes.The cohesive zone model (CZM) has found a wide acceptance as a tool for the simulation of debonding in adhesively bonded joints. This model is commonly used for the simulation of the quasi-static fracture problems, especially in the case of interface cracks such as in bonded joints and delamination in composites. The possibility to simulate the growth of a crack without any remeshing requirements and the relatively easy possibility to manipulate the constitutive law of the cohesive elements makes the cohesive zone model attractive also for the fatigue crack growth simulation.The purpose of this work is to develop the two-dimensional cohesive zone model presented by Pirondi and Moroni.A cohesive damage model has been implemented by means of the USDFLD and URDFIL subroutines in the commercial software Abaqus, in order to take into account the damage produced by fatigue loading.The CZ models were tested on various joint geometries characterized by different mixed mode ratios, in order to verify accuracy, robustness and performance in terms of computational time

Influence of geometrical imperfections and flaws at welds of steel liners on fatigue behavior of pressure tunnels and shafts in anisotropic rock

The recent development of high-strength (HSS) weldable steels has enlarged the range of design alternatives for the optimization of high-head steel-lined pressure tunnels and shafts (SLPT&S) in the hydropower industry. With the liberalization of the European energy market and increasing contribution of new renewable volatile energies in the electricity grid due to high subsidies, storage hydropower and pumped-storage plants are subject to more and more severe operation conditions resulting in more frequent transients. The use of HSS allows the design of thinner and thus more economic steel liners. However, welded HSS do not provide higher fatigue resistance than lower steel grades, and may be particularly subject to the risk of cold cracking in the weld material as dramatically illustrated by the failure of the Cleuson-Dixence pressure shaft in 2000. Fatigue behavior may become the leading limit state criterion. This research project aims at improving the comprehension of the mechanical behavior of SLPT&S and at developing a framework for probabilistic fatigue crack growth and fracture assessment of crack-like flaws in the weld material of longitudinal butt welded joints, considering all possible steel grades for high-head hydropower schemes. The influence of anisotropic rock behavior and geometrical imperfections at the longitudinal joints on the structural stresses have been studied by means of the finite element method accounting for the interaction with the backfill concrete-rock multilayer system. Parametric correction factors have been derived to estimate stress concentrations and structural stresses in steel liners with ease in practice, allowing the use of $S$-$N$ based engineering fatigue assessment approaches. Stress intensity factors (SIF) for axial cracks in the weld material of the longitudinal joints have also been obtained by means of computational linear elastic fracture mechanics (LEFM). The use of the previously developed parametric equations in the classical formulas for SIF in cracked plated structures has been validated, and new parametric equations for the weld shape correction have been proposed. A probabilistic model for fatigue crack growth assessment has been developed in the framework of LEFM in combination with the Paris-Erdogan law. The probability of failure is estimated by means of the Monte Carlo simulation procedure, in which the crack growth rate parameters and the crack shape ratio are defined as stochastic variables. A week-long normalized loading spectrum derived from prototype measurements on an alpine pumped-storage hydropower plant in Switzerland is used. This approach provides relative and quantitative results through parametric studies, giving new insights on the fatigue behavior of steel liners containing cracks in the weld material of the longitudinal joints. Finally, a fatigue assessment case study is presented, detailing the entire calculation procedures developed in this research. It aims at ensuring the transfer of knowledge toward practitioners

Fatigue crack propagation in functionally graded materials

Propagation of cracks in functionally graded materials (FGMs) under cyclic loading was investigated via experiments and finite element (FE) analysis. Alumina-epoxy composites with an interpenetrating-network structure and tailored spatial variation in composition were produced via a multi-step infiltration technique. Compressed polyurethane foam was infiltrated with alumina slip. After foam burn-out and sintering, epoxy was infiltrated into the porous alumina body. Non-graded specimens with a range of compositions were produced, and elastic properties and fatigue behaviour were characterised. An increase in crack propagation resistance under cyclic loading was quantified via a novel analytical approach. A simulation platform was developed with the commercial FE package ANSYS. Material gradient was applied via nodal temperature definitions. Stress intensity factors were calculated from nodal displacements near the crack-tip. Deflection criteria were compared and the local symmetry criterion provided the most accurate and efficient predictions. An automated mesh-redefinition algorithm enabled incremental simulation of crack propagation. Effects of gradient and crack-geometry parameters on crack-tip stresses were investigated, along with influences of crack-shape, crack-bridging, residual stresses and plasticity. The model provided predictions and data analysis for experimental specimens. Fatigue cracks in graded specimens deflected due to elastic property mismatch, concordant with FE predictions. In other FGMs, thermal or plastic properties may dominate deflection behaviour. Weaker step-interfaces influenced crack paths in some specimens; otherwise effects of toughness variation and gradient steps on crack path were negligible. Crack shape has an influence, but this is secondary to that of elastic gradient. Cracks in FGM specimens initially experienced increase in fatigue resistance with crack-extension followed by sudden decreases at step-interfaces. Bridging had a notable effect on crack propagation resistance but not on crack path. Similarly, crack paths did not differ between monotonic and cyclic loading, although crack-extension effects did. Recommendations for analysis and optimisation strategies for other FGM systems are given. Experimental characterization of FGMs is important, rather than relying on theoretical models. Opportunities for optimization of graded structures are limited by the properties of the constituent materials and resultant general crack deflection behaviour