Optimum Design of a Ring-Shaped Clip Gauge
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RESEARCH PAPER
Optimum Design of a Ring-Shaped Clip Gauge P. Thanakun 1 & J. Kasivitamnuay 1
&
P. Singhatanadgid 1
Received: 29 October 2019 / Accepted: 4 November 2020 # The Society for Experimental Mechanics, Inc 2020
Abstract The optimisation methodology was applied to design a specific geometry for a ring-shaped clip gauge as a quasi-static displacement measurement. The gauge was designed to maximise sensitivity under various types of constraints, including working range, strength, and installation. The analytical expressions of the ring gauge’s responses and constraints were derived to formulate an optimisation problem. The optimal solution was determined by an optimisation solver in the MathCAD Prime 4 program. The sensitivity of the objective function with respect to the parameters in the optimisation problem evaluated at the optimal solution was also determined. The sensitivity and linearity of the designed ring gauge is in the range of commercial gauges. The accuracy of the ring gauge was better than 0.1%, complying with ASTM standard E1820. Performance of the ring gauge, i.e. its linearity, hysteresis, and repeatability, was better than the DCB gauge reproduced from the standard. Applying the ring gauge to a tensile test with a cracked specimen yielded an accurate displacement measurement. Limitations of the analytical formulation are highlighted and recommendations for improving the formulation are discussed. Keywords Clip gauge . Optimisation . Strain gauge . Transducer
Introduction A clip gauge is a displacement transducer commonly used in fracture mechanics tests, including fracture toughness tests, the fatigue crack growth rate test, and the stress-corrosion crack growth rate test. The gauge can be used to measure crack-mouth opening displacement (CMOD) or load-line displacement (LLD) of a test specimen. This displacement is then used to calculate the crack-tip parameters and crack length. The working principle of a clip gauge is a spring force action due to a deformation of its body. The displacement of a gauge at the contact points with a specimen’s knife edges can be correlated with strains at any location of the gauge. The strain can be measured by a foil resistance strain gauge and is
* J. Kasivitamnuay [email protected] P. Thanakun [email protected] P. Singhatanadgid [email protected] 1
Department of Mechanical Engineering, Faculty of Engineering, Chulalongkorn University, Phayathai Rd., Wangmai, Bangkok, Pathumwan 10330, Thailand
typically measured at the location that maximises the gauge’s sensitivity. The first configuration design of a clip gauge was a doublecantilever beam (DCB) clip gauge. This type of gauge was developed for the KIc test [1] and was later adopted in the ASTM standard E399 [2]. To test the fracture toughness of a ductile material, the ASTM standard E1820 [3] recommended another design configuration for a DCB gauge with a larger measurement range. Smith et al. [4] studied the nonlinearity behaviour of various DCB gauge designs and reported that a combined
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