Hello, everybody.
I make mechanical tests of tension, compression or bending. Sometimes, the force-displacement diagrams are nonlinear and concave looking upward, under low loads. I have an explanation and a good mathematical model for this phenomenon, but my paper was rejected recently with the motive, that its literature review is too weak.
Could you help me with any references that touch this subject?
Dear Rumen
It is well known that the force-displacement diagrams of many ductile materials should manifest a linear relationship until the phenomenon of necking occurs. In this case, the yield strength of the materials has been reached, at which a non-linear behavior of the force-displacement begins to appear in the diagrams. The necking phenomenon can manifest itself at a low load especially when the cross section of the sample is a small one. I would assume that the appearance of a non-linear behavior at low loads,in the case you have presented, could be because the cross sectional area of the tested samples was small. As you know that stress=(load/cross sectional area).In other words, the smaller the cross sectional area of the tested sample the easer the non-linear behavior to be reached with low loads on the samples.
Thank you Khaled.
This "plastic" explanation is well known, but I should clear the term low load, which, for this question, means load - much smaller than the yield or break one.
Furthermore, the word displacement represents the deformation of the measured base length and it sometimes is not proportional with the strains of each material micro-volume, in this length.
Dear Rumen, the initial stage of loading, really, looks a non-linear. There are some reasons (partially, tribological factors) for this phenomenon such as a plastic crumpling of surface asperities, friction with slip in contact (for compression tests), straightening of specimen under tension, clearance in joints of testing machine and so). For example, an effect of friction on the mechanical characteristics of materials determined in experiments is discussed in the paper "The role of friction in mechanical testing of materials // Journal of Friction and Wear, 2002, Vol. 23, No. 3, pp. 98-102", The standards on mechanical tests may be cited too, because they note the peculiarities of initial stage of force-displacement diagrams, as well as some books: yandex.by/images › Experimental mechanics)
Best regards
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