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Article
Publication date: 1 January 2006

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 solder…

1015

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

Keywords

Article
Publication date: 1 April 1993

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 on the…

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

Keywords

Article
Publication date: 1 September 1949

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

Article
Publication date: 1 January 1949

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

Article
Publication date: 30 September 2014

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…

351

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

Keywords

Article
Publication date: 8 April 2022

Fuminobu Ozaki and Takumi Umemura

In this study, engineering stress-strain relationships considering an effect of strain rate on steel materials at elevated temperatures were formulated and a simplified analytical…

Abstract

Purpose

In this study, engineering stress-strain relationships considering an effect of strain rate on steel materials at elevated temperatures were formulated and a simplified analytical model using a two-dimensional beam element to analytically examine the effect of strain rate on the load-bearing capacity and collapse temperature was proposed.

Design/methodology/approach

The stress-strain relationships taking into account temperature, strain, and strain rate were established based on the past coupon test results with strain rate as the test parameter. Furthermore, an elasto-plastic analysis using a two-dimensional beam element, which considered the effect on strain rate, was conducted for both transient- and steady-state conditions.

Findings

The analytical results agreed relatively well with the test results, which used small steel beam specimens with a rectangular cross-section under various heating rates (transient-state condition) and deformation rates (steady-state condition). It was found that the bending strength and collapse temperature obtained from the parametric analyses agreed relatively well with those evaluated using the effective strength obtained from the coupon tests with strain equal to 0.01 or 0.02 under the fast strain rates.

Originality/value

The effect of stress degradation, including the stress-strain relationships at elevated temperature, was mitigated by considering the effect of strain rate on the analytical model. This is an important point to consider when considering the effect of strain rate on steel structural analysis at elevated temperatures to maintain analytical stability unaccompanied by the stress degradation.

Article
Publication date: 12 April 2022

Qing-Yun Deng, Shun-Peng Zhu, Jin-Chao He, Xue-Kang Li and Andrea Carpinteri

Engineering components/structures with geometric discontinuities normally bear complex and variable loads, which lead to a multiaxial and random/variable amplitude stress/strain

Abstract

Purpose

Engineering components/structures with geometric discontinuities normally bear complex and variable loads, which lead to a multiaxial and random/variable amplitude stress/strain state. Hence, this study aims how to effectively evaluate the multiaxial random/variable amplitude fatigue life.

Design/methodology/approach

Recent studies on critical plane method under multiaxial random/variable amplitude loading are reviewed, and the computational framework is clearly presented in this paper.

Findings

Some basic concepts and latest achievements in multiaxial random/variable amplitude fatigue analysis are introduced. This review summarizes the research status of four main aspects of multiaxial fatigue under random/variable amplitude loadings, namely multiaxial fatigue criterion, method for critical plane determination, cycle counting method and damage accumulation criterion. Particularly, the latest achievements of multiaxial random/variable amplitude fatigue using critical plane methods are classified and highlighted.

Originality/value

This review attempts to provide references for further research on multiaxial random/variable amplitude fatigue and to promote the development of multiaxial fatigue from experimental research to practical engineering application.

Details

International Journal of Structural Integrity, vol. 13 no. 3
Type: Research Article
ISSN: 1757-9864

Keywords

Article
Publication date: 1 June 1956

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 matters of…

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

Article
Publication date: 1 July 1951

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 maximum…

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

Article
Publication date: 13 June 2016

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

Keywords

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