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The purpose of this paper is to investigate the strain distribution, stress-based fracture limit and corrosion behaviour of titanium Grade 2 sheets during single point incremental forming (SPIF) process, with various computerized numerical control (CNC) spindle rotational speeds and step depths. The development of corrosion pits in 3.5 (%) NaCl solution has also been studied during the SPIF process.

A potentiodynamic polarization (PDP) study was performed to investigate the corrosion behaviour of titanium Grade 2 deformed samples, with various spindle rotational speeds in 3.5 (%) NaCl solution. The scanning electron microscope (SEM) and transmission electron microscope (TEM) analysis was carried out to study the fracture behaviour, dislocation densities and corrosion morphology of deformed samples.

The titanium Grade 2 sheets exhibited better strain distribution, fracture limit and corrosion resistance by increasing the CNC spindle rotational speeds, tool diameters and vertical step depths (VSD). It was recorded that varying the spindle speed affected plastic deformation which in turn affected corrosion rate.

In this study, poor corrosion rate was observed for the as-received condition, and better corrosion rate was achieved at maximum speed of 600 rpm and 0.6 mm of VSD in the deformed sheet. This indicates that corrosion rate improved with increase in the plastic deformation. The EDS analysis report of corroded surface revealed the composition to be mainly of titanium and oxides.

This study discusses the strain distribution, stress-based fracture limit and corrosion behaviour by using titanium Grade 2 sheets during SPIF process.

This study is useful in the field of automobile and industrial applications.

With an increase in the spindle rotational speeds and VSD, the titanium Grade 2 sheets showed better strain distribution, fracture limit and corrosion behaviour; the same is evidenced in fracture limit curve and PDP curves.

The objective of this work is to develop an element technology to recover the plane stress response without any plane stress specific modifications in the large strain regime. Therefore, the essential feature of the proposed element formulation is an interface to arbitrary three‐dimensional constitutive laws. The easily implemented and computational cheap four‐noded element is characterized by coarse mesh accuracy and the satisfaction of the plane stress constraint in a weak sense. A number of example problems involving arbitrary small and large strain constitutive models demonstrate the excellent performance of the concept pursued in this work.

The purpose of this paper is to carry out a delamination fracture analysis of the three-dimensional functionally graded split cantilever beam (SCB) configuration.

The fracture behaviour was studied analytically in terms of the strain energy release rate by applying methods of linear elastic fracture mechanics. It was assumed that the material is functionally graded along the beam width, height and length. The strain energy release rate was derived by analysing the stress and strain state in the beam cross-sections ahead and behind the crack front. An additional analysis of the strain energy release rate was performed by considering the beam strain energy for verification.

The influence of material gradient along the beam width, height and length on the delamination fracture behaviour was investigated. The effect of crack length was analysed too. The analytical approach developed is very useful for parametric fracture investigations. The results obtained in the present study can be applied for optimisation of three-dimensional functionally graded beam systems in their design with respect to delamination fracture behaviour.

An analytical approach for studying the delamination fracture in the SCB configuration that is functionally graded along the beam width, height and length was developed.

The purpose of this paper is to investigate the use of nanoindentation with a Berkovich indenter as a method of extracting equivalent stress‐strain curves for the base metal and the welded zone of a friction stir welded aluminum alloy.

Friction stir welding is a solid‐state joining process, which emerged as an alternative technique to be used in high strength alloys that were difficult to join with conventional joining techniques. This technique has a significant effect on the local microstructure and residual stresses combined with deformation. Nano‐ and micro‐indentation are the most commonly used techniques to obtain local mechanical properties of engineering materials. In order to test the reliability of nanoindentation technique and to connect nanoscale with macroscale, the indentation hardness‐depth relation established by Nix and Gao was applied on the experimental values.

The predictions of this model were found to be in good agreement with classical hardness measurements on AA 6082‐T6 aluminum alloy. Also, finite element method provides a numerical tool to calculate complex nanoindentation problems and in correlation with gradients theories forms a well‐seried tool in order to take into account size effects.

By studying this alloy, the paper reviews fundamental principles such as stress‐strain distribution, size effects rise during nanoindentation and the applicability of finite element method, in order to take into account these issues.

This paper aims to present an effective sensing detection system based on fiber Bragg grating (FBG) sensing technology for protective barriers that have been effectively applied to intercept and stop rocks from falling onto railway tracks. . Determination of exact stress and deformation values during impact tests for key components of the protective barrier forms important criteria for quality control of these barriers. Monitoring changes in force along the protective barrier when deployed in field application allows for real-time disaster warning for collapse and falling rocks.

In this paper, we propose a monitoring strategy for key components of a protective barrier. During performance tests, dynamic force and strain were measured for the steel strands and supporting I-beam, respectively. Design of a special elastic structure for the force transducer based on finite element analysis and tensile tests has been discussed here. Two types of FBG force transducers were manufactured based on the elastic structure. Four FBG force transducers and four FBG strain sensors were used for impact verification testing of a new rigid protective barrier with a design protection level of 25 KJ.

Dynamic force and strain responses were obtained during an impact of free-falling block with a kinetic energy of 25 KJ.

The FBG monitoring scheme can be extremely valuable for optimized design of the barrier and can provide real-time disaster warning in regions of collapse and falling rocks.

Three main subjects are presented in this paper: (i) A description of tests made for the purpose of determining design data; (ii) a discussion of the problems arising in the establishment of the approval procedures necessary to ensure safety and reliability; and (iii) a discussion of proposals for cyclic reliability tests. In the first section, tests to provide design data for glazing materials are described with particular emphasis placed on glasses. Types of specimen and apparatus for obtaining data at room temperature are mentioned and illustrations given of apparatus and specimens used in long term elevated temperature tests. In the second section, the overall level of reliability of complete components is discussed both in terms of structural safety and satisfactory service. While the current requirements have proved satisfactory for the past generation of aircraft, proposals are now put forward for patterns of testing that are more closely linked to the various design conditions now in use with both high‐speed and low‐speed aircraft, in order to place equal importance on the effects of temperature. In the third section, proposals are put forward for cyclic testing to overcome what appears to be an increasingly unsatisfactory record of reliability. The purpose of the tests is not to establish a safe life for any particular design but to reveal design deficiencies occurring from repeated applications of flight and thermal loadings.

The effect of bending is investigated through the comparison of the membrane analysis and the shell analysis for stretching and deep drawing. An incremental formulation incorporating the effect of shape change and anisotropy is used for the analysis of elastic‐plastic non‐steady large deformation. The deformation during a step is considered using the natural convected coordinate system. Stretching of a square blank with a hemispherical punch and deep drawing of a cyclindrical cup is analysed and the corresponding experiments are carried out. The computational results are compared with the experiments. In stretching, the comparison has shown that both the membrane analysis and the shell analysis are in good agreement with the experiment for punch load and strain distribution. In deep drawing, the computed loads of both the membrane analysis and the shell analysis are generally in good agreement with the experiment. The computed thickness strain of the membrane analysis, however, shows a wide difference with the experiment. In the shell analysis, the thickness strain shows good agreement with the experiment. It has been shown that the membrane approach shows a limitation for the deep drawing process in which the effect of bending is not negligible and more exact informations on the thickness strain distribution are required.

Recently, a new class of fatigue crack growth models based on elastoplastic stress‐strain histories at the crack tip region and strain‐life fatigue damage models have been proposed. The fatigue crack propagation is understood as a process of continuous crack initializations, over elementary material blocks, which may be governed by strain‐life data of the plain material. The residual stresses developed at the crack tip play a central role in these models, since they are used to assess the actual crack driving force, taking into account mean stresses and loading sequential effects. The UniGrow model fits this particular class of fatigue crack propagation models. The purpose of this paper is to propose an extension of the UniGrow model to derive probabilistic fatigue crack propagation data, in particular the derivation of the P–da/dN–ΔK–R fields.

An existing deterministic fatigue crack propagation model, based on local strain‐life data is first assessed. In particular, an alternative methodology for residual stress computation is proposed, based on elastoplastic finite element analysis, in order to overcome inconsistencies found in the analytical approximate approaches often used in literature. Then, using probabilistic strain‐life fields, a probabilistic output for the fatigue crack propagation growth rates is generated. A new probabilistic fatigue field is also proposed to take mean stress effects into account, using the Smith‐Watson‐Topper (SWT) damage parameter. The proposed models are assessed using experimental data available for two materials representative from old Portuguese bridges.

A new method to generate probabilistic fatigue crack propagation rates (P–da/dN–ΔK–R fields) is proposed and verified using puddle iron from old Portuguese bridges, usually characterized by significant scatter in fatigue properties. Also, a new probabilistic fatigue field for plain material is proposed to deal with mean stress effects.

A relation between the P–ε–N and the P–da/dN–ΔK–R fields is firstly proposed in this research. Furthermore, a new P–SWT–N field is proposed to deal with mean stress effects.

The purpose of this paper is to deal with large deformation analysis of plane beams composed of functionally graded (FG) elastic material with a variable Poisson’s ratio.

The material is assumed to be linear elastic, with a Poisson’s ratio varying according to a power law along the thickness direction. The finite element used is a plane beam of any-order of approximation along the axis, and with four transverse enrichment schemes, which can describe constant, linear, quadratic and cubic variation of the strain along the thickness direction. Regarding the constitutive law, five materials are adopted: two homogeneous limiting cases, and three intermediate FG cases. The effect of both finite element kinematics and distribution of Poisson’s ratio on the mechanical response of a cantilever is investigated.

In accordance with the scientific literature, the second scheme, in which the transverse strain is linearly variable, is sufficient for homogeneous long (or thin) beams under bending. However, for FG short (or moderate thick) beams, the third scheme, in which the transverse strain variation is quadratic, is needed for a reliable strain or stress distribution.

In the scientific literature, there are several studies regarding nonlinear analysis of functionally graded materials (FGMs) via finite elements, analysis of FGMs with constant Poisson’s ratio, and geometrically linear problems with gradually variable Poisson’s ratio. However, very few deal with finite element analysis of flexible beams with gradually variable Poisson’s ratio. In the present study, a reliable formulation for such beams is presented.

The purpose of this paper is to provide a method to predict the situation of a loaded element in the compressive stress curve to prevent failure of crucial elements in load-bearing masonry walls and to propose a material model to simulate a compressive element successfully in Abaqus software to study the structural safety by using non-linear finite element analysis.

A Weibull distribution function was rewritten to relate between failure probability function and axial strain during uniaxial compressive loading. Weibull distribution parameters (shape and scale parameters) were defined by detected acoustic emission (AE) events with a linear regression. It was shown that the shape parameter of Weibull distribution was able to illustrate the effects of the added fibers on increasing or decreasing the specimens’ brittleness. Since both Weibull function and compressive stress are functions of compressive strain, a relation between compressive stress and normalized cumulative AE hits was calculated when the compressive strain was available. By suggested procedures, it was possible to monitor pretested plain or random distributed short fibers reinforced adobe elements (with AE sensor and strain detector) in a masonry building under uniaxial compression loading to predict the situation of element in the compressive stress‒strain curve, hence predicting the time to element collapse by an AE sensor and a strain detector. In the predicted compressive stress‒strain curve, the peak stress and its corresponding strain, the stress and strain point with maximum elastic modulus and the maximum elastic modulus were predicted successfully. With a proposed material model, it was illustrated that the needed parameters for simulating a specimen in Abaqus software with concrete damage plasticity were peak stress and its corresponding strain, the stress and strain point with maximum elastic modulus and the maximum elastic modulus.

The AE cumulative hits versus strain plots corresponding to the stress‒strain curves can be divided into four stages: inactivity period, discontinuous growth period, continuous growth period and constant period, which can predict the densifying, linear, non-linear and residual stress part of the stress‒strain relationship. By supposing that the relation between cumulative AE hits and compressive strain complies with a Weibull distribution function, a linear analysis was conducted to calibrate the parameters of Weibull distribution by AE cumulative hits for predicting the failure probability as a function of compressive strain. Parameters of m and θ were able to predict the brittleness of the plain and tire fibers reinforced adobe elements successfully. The calibrated failure probability function showed sufficient representation of the cumulative AE hit curve. A mathematical model for the stress–strain relationship prediction of the specimens after detecting the first AE hit was developed by the relationship between compressive stress versus the Weibull failure probability function, which was validated against the experimental data and gave good predictions for both plain and short fibers reinforced adobe specimens. Then, the authors were able to monitor and predict the situation of an element in the compressive stress‒strain curve, hence predicting the time to its collapse for pretested plain or random distributed short fibers reinforced adobe (with AE sensor and strain detector) in a masonry building under uniaxial compression loading by an AE sensor and a strain detector. The proposed model was successfully able to predict the main mechanical properties of different adobe specimens which are necessary for material modeling with concrete damage plasticity in Abaqus. These properties include peak compressive strength and its corresponding axial strain, the compressive strength and its corresponding axial strain at the point with maximum compressive Young’s modulus and the maximum compressive Young’s modulus.

The authors were not able to decide about the effects of the specimens’ shape, as only cubic specimens were chosen; by testing different shape and different size specimens, the authors would be able to generalize the results.

The paper includes implications for monitoring techniques and predicting the time to the collapse of pretested elements (with AE sensor and strain detector) in a masonry structure.

This paper proposes a new method to monitor and predict the situation of a loaded element in the compressive stress‒strain curve, hence predicting the time to its collapse for pretested plain or random distributed short fibers reinforced adobe (with AE sensor and strain detector) in a masonry building under uniaxial compression load by an AE sensor and a strain detector.