Critical Strain Determination Based on the Euler-Fresnel Jig

When considering a composite strip or plate under certain thermal and environmental conditions and loadings, there is a minimum strain threshold for the appearance of the first micro crack. The associated strain level is defined here as “critical strain”. There are various active displacement methods to measure this strain level (by tension and bending). The registration of the first micro crack is however challenging. Therefore, some alternative methods have been developed like the Bergen ellipse [1]. With this method, a relatively thin strip is forced by clamping to “follow” the elliptical contour of the jig. The strip undergoes various strain levels from 0% to 2% or 3%. However, the strain distribution as a function of the strip length is far from linear. This causes inaccurate readings and high error sensitivity for certain areas on the ellipse. To overcome this problem, a novel jig design is introduced here; this design is based on a perfectly linear strain distribution along the strip’s length. The resulting curve is a classical one known as the Euler-Fresnel curve [2]. The linearity and the constant, low sensitivity to measurement errors guarantees high accuracy. Only at the beginning and the end of the strip, the measured strain might deviate from the real one, especially when the thickness of the strip is moderately less (Dh > 0.1 [mm]) than the height of the slot, Figure 9. The jig is a low cost device that can easily be placed in climate cabinets for e.g. cryo-cycling. In this paper we focus on the mathematical derivation of the jig, compare it to the Bergen ellipse, and provide the full consideration of the associated primary and secondary forces and moments. In addition, a comprehensive strength analysis of various lay-ups is provided for the maximum strain level of 2%. The paper ends with some key conclusions and recommendations.