The proper answer lies in meaning of the word self limiting and the nature of secondary stress. With secondary stress, not only the word self limiting comes but also "absence of gross plastic deformation" and "redistribution" of load comes.

In case of primary stress ( load driven) the displacement can be uncontrolled depending on the magnitude of loading.However in case of displacement control, the displacement is actually "controlled" and hence cannot be infinite.In the example of pressure elongation, if the pressure magtitude is high, the pipe can undergo bursting failure.This would happen if an uncontrolled magnitude of pressure is applied.However if the pipe has not undergone bursting, the pressure is obviously not of "that magnitude to create an uncontrolled displacement". The displacement that this pressure imposes on the system is again a "controlled" one.This is the basic difference in pressure applied as a load and the pressure induced displacement imposed on a system.

This however does not indicate why it should be self limiting and what exactly is self limiting and how the other terms in the definition of secondary stress come.

The pressure elongation will obviously not produce gross plastic deformation , as it that has to happen the "uncontrolled" pressure would have done it.

The load deformation relation is P=KD where symbols have usual meaning.

For non linearity , K is a function of D. Non linearity can be in three different forms material ( plasticity),geometric ( load and stress can change depening on the geometric deformation) and contact ( a very simple example, a guide with gap)all may act together or individually.

If load imposed is constant, it will not reduce on its own i.e. a 500N applied will not on its own become 450N.

However if displacement is the input and since in non iinearity K is a function of D ( and sometimes P also is a function of D) and as K drops, say due to plasticity or other two forms of non linearity ( a classic example of geometric non linearity is a volter's pole which resists load with membrane or bending action depending on whether the pole is straight or bent), the developed load drops.

In the above discussion, we have already seen that the pressure elongation will not cause uncontrolled deformation unless the pressure itself is very high which will result in a bursting type failure. Now, when the elongation happens and it is restrained ( if there is no restraint, there is no stress generated), stresses will be generated.How and why will they be self limiting?

The answer lies in the mathematical expression above that if D is applied, P generated can reduce if K reduces due to all/any form of non linearity.

Hence it has the characterestic of self limiting.

The self limiting parameter also has the term "redistrubution" associated with it as due to change in K there is redistribution of load in a system with stiffer parts taking higher loads.

Hence the pressure induced elongation is a secondary stress.

The concept of self limiting was wonderfully explained to me by Mr. Thomas J Vaan Laan.I was fortunate enough to learn this thing from him.

Regards