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Article

H. Rhee and K.N. Subramanian

To understand the roles of service‐related parameters, such as imposed cyclic strain amplitude and cyclic strain rate, on the stress relaxation behaviour of eutectic Sn‐Ag…

Abstract

Purpose

To understand the roles of service‐related parameters, such as imposed cyclic strain amplitude and cyclic strain rate, on the stress relaxation behaviour of eutectic Sn‐Ag solder joints.

Design/methodology/approach

Cyclic shear straining with associated stress relaxation at the shear strain extremes imposed was carried out on pre‐strained eutectic Sn‐Ag solder joints with various cyclic shear straining conditions. Results from such experiments were compared with previously reported findings from monotonic shear straining and stress relaxation tests.

Findings

At higher testing temperatures with a larger cyclic strain amplitude, stress states realized at the subsequent cycle are comparable with, or even gradually increase on, those experienced at the previous cycle, especially after few cycles. The maximum shear stress obtained at each cycle and residual stress during stress relaxation are strongly affected by cyclic strain rate. Stress relaxation during subsequent cycles of straining was found to be strongly dependent on the test temperature, and the imposed cyclic strain amplitude and cyclic strain rate.

Originality/value

In this paper, the experiments were carried out on eutectic Sn‐Ag solder joints with about a 100 μm joint thickness, which are, therefore, representative of those used in microelectronics. Also, there is no systematic study reporting the effects of cyclic straining conditions on the stress relaxation behaviour of eutectic Sn‐Ag solder for this joint configuration in the published literature.

Details

Soldering & Surface Mount Technology, vol. 18 no. 1
Type: Research Article
ISSN: 0954-0911

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Article

Y. TSUI and Y.M. CHENG

Large strain model can be formulated in terms of the Lagrangian or the Eulerian frame. In this paper, the Eulerian type large strain models are studied. Numerical examples…

Abstract

Large strain model can be formulated in terms of the Lagrangian or the Eulerian frame. In this paper, the Eulerian type large strain models are studied. Numerical examples on the Lagrangian and Eulerian types large strain models are investigated and compared. It is found that the differences in the choice of large strain model under large strain and rotation problems are noticeable but not significant if small load step is used for analysis. Furthermore, we have also found that unsymmetrical formulation instead of symmetrical formulation should be adopted for Eulerian type large strain models.

Details

Engineering Computations, vol. 10 no. 4
Type: Research Article
ISSN: 0264-4401

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Article

A.E. Johnson

A SURVEY has been made of some aspects of behaviour of metals under multiaxial stress systems, taking into consideration available experimental evidence.

Abstract

A SURVEY has been made of some aspects of behaviour of metals under multiaxial stress systems, taking into consideration available experimental evidence.

Details

Aircraft Engineering and Aerospace Technology, vol. 21 no. 9
Type: Research Article
ISSN: 0002-2667

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Article

THE work described in this paper is part of a programme concerned with the plastic, creep, and relaxation properties of metals under complex stress systems at elevated…

Abstract

THE work described in this paper is part of a programme concerned with the plastic, creep, and relaxation properties of metals under complex stress systems at elevated temperatures.which is being carried out in the Engineering Division of the N.P.L. It comprises data on the criterion of departure from elastic behaviour, of a low carbon steel over the temperature range 20–550 deg. C, and of an aluminium alloy over the temperature range 20–200 deg. C, and the creep properties under complex stress systems of the low carbon steel at 350 deg. C, and of the aluminium alloy at 150 and 200 deg. C.

Details

Aircraft Engineering and Aerospace Technology, vol. 21 no. 1
Type: Research Article
ISSN: 0002-2667

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Article

Denise Ferreira, Jesús Bairán, Antonio Marí and Rui Faria

A nonlinear finite element (FE) beam-column model for the analysis of reinforced concrete (RC) frames with due account of shear is presented in this paper. The model is an…

Abstract

Purpose

A nonlinear finite element (FE) beam-column model for the analysis of reinforced concrete (RC) frames with due account of shear is presented in this paper. The model is an expansion of the traditional flexural fibre beam formulations to cases where multiaxial behaviour exists, being an alternative to plane and solid FE models for the nonlinear analysis of entire frame structures. The paper aims to discuss these issues.

Design/methodology/approach

Shear is taken into account at different levels of the numerical model: at the material level RC is simulated through a smeared cracked approach with rotating cracks; at the fibre level, an iterative procedure guarantees equilibrium between concrete and transversal reinforcement, allowing to compute the biaxial stress-strain state of each fibre; at the section level, a uniform shear stress pattern is assumed in order to estimate the internal shear stress-strain distribution; and at the element level, the Timoshenko beam theory takes into account an average rotation due to shear.

Findings

The proposed model is validated through experimental tests available in the literature, as well as through an experimental campaign carried out by the authors. The results on the response of RC elements critical to shear include displacements, strains and crack patterns and show the capabilities of the model to efficiently deal with shear effects in beam elements.

Originality/value

A formulation for the nonlinear shear-bending interaction based on the fixed stress approach is implemented in a fibre beam model. Shear effects are accurately accounted during all the nonlinear path of the structure in a computationally efficient manner.

Details

Engineering Computations, vol. 31 no. 7
Type: Research Article
ISSN: 0264-4401

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Article

A.E. Johnson

TURBINE disks of jet propulsion units operate under conditions of considerable complexity for which steam turbine practice and experience afford little assistance in…

Abstract

TURBINE disks of jet propulsion units operate under conditions of considerable complexity for which steam turbine practice and experience afford little assistance in matters of calculation and design.

Details

Aircraft Engineering and Aerospace Technology, vol. 28 no. 6
Type: Research Article
ISSN: 0002-2667

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Article

M. Ish‐Horowicz

IN modern structural design the maximum carrying capacity of a member under non‐uniform static stress at normal temperatures is not necessarily the load which gives a…

Abstract

IN modern structural design the maximum carrying capacity of a member under non‐uniform static stress at normal temperatures is not necessarily the load which gives a maximum stress equal to that at the limit of proportionality. All experiments have shown the ultimate strength of beams to exceed the value predicted on the basis of the elastic theory. This applies to simply supported and redundant beams made of steel and wrought iron, as well as to beams constructed from other metals such as cast iron, aluminium, magnesium, etc. Investigators differ, however, in the interpretation of this increased strength and in their methods of a more advantageous use of the material. These are usually based on specific experiments and apply to certain conditions only, without embracing all materials and all possible load distributions and types of structures.

Details

Aircraft Engineering and Aerospace Technology, vol. 23 no. 7
Type: Research Article
ISSN: 0002-2667

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Article

Vladimir Kobelev

The purpose of this paper is to develop the method for the calculation of residual stress and enduring deformation of helical springs.

Abstract

Purpose

The purpose of this paper is to develop the method for the calculation of residual stress and enduring deformation of helical springs.

Design/methodology/approach

For helical compression or tension springs, a spring wire is twisted. In the first case, the torsion of the straight bar with the circular cross-section is investigated, and, for derivations, the StVenant’s hypothesis is presumed. Analogously, for the torsion helical springs, the wire is in the state of flexure. In the second case, the bending of the straight bar with the rectangular cross-section is studied and the method is based on Bernoulli’s hypothesis.

Findings

For both cases (compression/tension of torsion helical spring), the closed-form solutions are based on the hyperbolic and on the Ramberg–Osgood material laws.

Research limitations/implications

The method is based on the deformational formulation of plasticity theory and common kinematic hypotheses.

Practical implications

The advantage of the discovered closed-form solutions is their applicability for the calculation of spring length or spring twist angle loss and residual stresses on the wire after the pre-setting process without the necessity of complicated finite-element solutions.

Social implications

The formulas are intended for practical evaluation of necessary parameters for optimal pre-setting processes of compression and torsion helical springs.

Originality/value

Because of the discovery of closed-form solutions and analytical formulas for the pre-setting process, the numerical analysis is not necessary. The analytical solution facilitates the proper evaluation of the plastic flow in torsion, compression and bending springs and improves the manufacturing of industrial components.

Details

Multidiscipline Modeling in Materials and Structures, vol. 16 no. 3
Type: Research Article
ISSN: 1573-6105

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Article

Fatemeh FaghihKhorasani, Mohammad Zaman Kabir, Mehdi AhmadiNajafabad and Khosrow Ghavami

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…

Abstract

Purpose

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.

Design/methodology/approach

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 stressstrain curve, hence predicting the time to element collapse by an AE sensor and a strain detector. In the predicted compressive stressstrain 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.

Findings

The AE cumulative hits versus strain plots corresponding to the stressstrain 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 stressstrain 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 stressstrain 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 stressstrain 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.

Research limitations/implications

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.

Practical implications

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.

Originality/value

This paper proposes a new method to monitor and predict the situation of a loaded element in the compressive stressstrain 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.

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Article

Feifei Zhang, Jieshi Chen and Jun Chen

– The purpose of this paper is to analyze theoretically the influence of normal stress on the formability of aluminum alloy sheets in non-linear strain paths.

Abstract

Purpose

The purpose of this paper is to analyze theoretically the influence of normal stress on the formability of aluminum alloy sheets in non-linear strain paths.

Design/methodology/approach

Four loading modes of non-linear strain paths are investigated in detail to consider the effect of normal stress on formability of aluminum alloy sheets.

Findings

Results show that the influence of normal stress in the first stage can be ignored. However, the normal stress in the second stage enhances the formability of aluminum alloy sheets obviously. Besides, the normal stress in the second stage is found to have larger effect on forming limit stress than that in the first stage.

Research limitations/implications

Maybe more experiment data should be obtained to support the theoretical findings.

Originality/value

This current study provides a better understanding of normal stress effect on the formability of aluminum alloy sheets in non-linear strain paths. Since the reacting stage of normal stress play important roles in normal stress effect on the formability of aluminum alloy sheets, the insight obtained in this paper will help to judge the instability of aluminum alloy sheets in complex forming processes with normal stress reacting on the sheet or tube.

Details

Engineering Computations, vol. 33 no. 4
Type: Research Article
ISSN: 0264-4401

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