Unified formulation for ultimate capacity of shear failure of arc spot welding using genetic programming

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Abstract

This study addresses genetic programming (GP) for the formulation of ultimate capacity of shear failure of arc spot welding. The proposed GP formulation is based on experimental results. The ultimate shear capacity of arc spot welding is formulated in terms of tensile strength, average welding thickness and diameter. The results of the proposed GP model are later compared with results of existing codes and are found to more accurate. In existing design codes four different equations are used whereas the proposed GP model is a unified formulation valid for all governing shear failures at the same time.

Introduction

Welding is a very effective means to connect two or more pieces of material together. The four most commonly used welding processes are shielded metal arc welding (SMAW), submerged arc welding (SAW), gas metal arc welding (GMAW), and flux core arc welding (FCAW) (Chen, 1999).

Among these processes arc spot welding (Fig. 1) has become popular recently due to its ability to spot weld from one side of the work as a fast method of producing multiple spot welds with a high degree of reproducibility. Arc spot welding is a MIG/MAG method intended to produce spot welds. The welding torch has a gas nozzle with support legs, and the welding time is controlled by a timer. The resulting welds are often overlap joints, as produced by conventional resistance spot welding. However, in this case, the workpiece needs to be accessible from both sides (Merritt and Ricketts, 2001, Weman, 2003).

In comparison with continuous welding, the process has the following advantages (Merritt and Ricketts, 2001, Weman, 2003):

  • •

    less heating and distortion;

  • •

    very simple to operate: simply position and press;

  • •

    lower, better-shaped convexity, particularly when welding thin sheet.

Section snippets

Nominal strength of arc spot welds

Welds used for cold-formed steel construction may be classified as arc welds (or fusion welds) and resistance welds. Arc welding is usually used for connecting cold-formed steel members to each other as well as connecting such thin members to heavy, hot-rolled steel framing members. It is used for groove welds, arc spot welds, arc seam welds, fillet welds, and flare groove welds. The AISI design provisions for welded connections are applicable only for cold-formed steel structural members, in

Background on genetic programming (GP)

GP is an extension to genetic algorithms proposed by Koza (Koza, 1992). Koza, the early pioneer defines GP as a domain-independent problem-solving approach in which computer programs are evolved to solve, or approximately solve, problems based on the Darwinian principle of reproduction and survival of the fittest and analogs of naturally occurring genetic operations such as crossover (sexual recombination) and mutation. GP reproduces computer programs to solve problems by executing the

Numerical application

The main focus of this study is an alternative shear strength formulation of arc spot welds using GP based on realistic experimental values. Therefore, an extensive literature survey has been performed for available experimental results. Experimental results (119 tests) in Table A1 taken from reference (McGuire and Peköz, 1979) given with related material parameters were used as training and test sets for GP formulation. The datasets for test and training are randomly selected among

Explicit formulation of GP model

Fig. 4 shows the expression tree (ET) of the formulation which is actually:Pn(GP)=(d(2)*(G1C8+d(2)))*(sin(d(2))−tan(d(3)))*(G2C7+sin((d(3)−G2C9)*d(1))*cos((G2C0*d(2)))*tan(sin(sqrt(sin(d(2)+d(2)))))tan(sqrt(d(3)))whered(1)=Fu;d(2)=d;d(3)=tavand constants of the equation areG1C8=1.898;G2C7=6.795;G2C9=2.89;G2C0=2.525Putting the corresponding values, the final equation becomes (given as MATLAB Code):Pn(GP)=((Fu*(1.898+d))*(sin(d)−tan(tav)))*(6.795+(sin((tav−2.89)*d(1))*cos((2.525*d)))*tan

Conclusion

This study proposes a new approach for the formulation of nominal shear strength of arc spot welding based on GP. Mainly four different failure types are observed for arc spot welding regarding shear failure. Thus the nominal shear strength of arc spot welding is calculated according to the governing failure equation presented in Eq. (1) of AISI (AISC, 1999). This study presents a unified formulation based on GP being valid for all shear failure types at the same time. The results of the

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