Hardening slope

The yield point and hardening slope of the interlayer should be low compared to those of the matrix material. 

To see what is going on physically, it is easier to return to our first condition. At low stress, if we make a little neck, the material in the neck will work-harden and will be able to carry the extra stress it has to stand because of its smaller area load will therefore be continuous, and the material will be stable. At high stress, the rate of workhardening is less as the true stress-true strain curve shows i.e. the slope of the o/e curve is less. Eventually, we reach a point at which, when we make a neck, the workhardening is only just enough to stand the extra stress. This is the point of necking, with... 

Gehange, n. slope hanging, pendant, gehiirtet, p.p. (of harten) hardened. 

The rate of strain hardening, do /ds, at any given value of the true stain is given by the slope of the true stress-true strain plot at that strain and is called the modulus of strain hardening. 

A plot of log o against log s should thus yield a straight line whose slope is n and which makes an intercept equal to log fej on the log o axis (at s = 1). Thus the constant kj represents the true stress at unit true strain and is termed the strength coefficient. The exponent n is known as the strain hardening exponent. 

For sites on very arid land or on steep slopes, an armoring system, or hardened cap, may be more effective than a vegetative layer for securing a landfill. Operators should not depend on an agricultural layer for protection in areas where vegetation cannot survive. Many States allow asphalt caps as an alternative to vegetative covers. Some closures at industrial sites have involved constructing... 

For steel, the modulus of elasticity is the same in the elastic region and yield plateau for static and dynamic response. In the strain hardening region the slope of the stress-strain curve is different for static and dynamic response, although this difference is not important for most structural design applications. 

In a constant strain-rate experiment, the rapid multiplication of dislocations following the yield point can produce more mobile dislocations than are necessary to maintain the imposed strain-rate and consequently the stress drops. The deformation will continue at a constant stress provided any decrease in u is compensated by an increase in iom, or vice versa. However, in general, the stress rises with increasing strain. The slope (dajdt) of the stress-strain curve is determined by the competition between two dislocation processes namely, work-hardening and recovery, which we now consider briefly. 

For a power-hardening material that obeys the stress-strain relationship, a = ke", where n is the strain-hardening exponent, the slope of the stress-strain curve is given by Eqn. (5.8) ... 

The constant X represents the slope of the isotropic mechanical response plotted in the (v,ln p lp f)-plane. By differentiating (4) and using (6) one can deduce the incremental hardening/softening law... 

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