A parallel spring model is proposed in order to discuss the thermal stress of drawn fibers. It is composed of N springs, each of which is fixed by a hook and bears a force in proportion to the strain. Since some springs are stretched and others are contracted, the total force of these springs is zero in a equilibrium state. With increased temperature some of springs detach from the hook and lose the force.
We assume here that the strain of springs is distributed and the spring detaches from the hook in the order of the rate of contraction, ie. the higher the contraction, the lower is the temperature at which the detaching occurs. Detaching from the hook of the contractive springs causes decrease in the extensile force and causes the contractive force in this model. This contractive force is a function of temperature. We calculated the function from this model.
The behaviors expected from this model are as follows:
1) The thermal stress-temperature relation is parabolic.
2) The relation between maximum thermal stress and temerature is parabolic when the cramp length varies.
3) The thermal stress-temperature relation varies with a strain distribution of the spring.