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softening region
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  软化区
    This theory can predict the initiation,de-velopment and localization of the softening region in the dynamically loaded beams,with avery good agreement with the experimental observation of pipe-whip tests.
    这一理论模型能够预报软化区的萌生、发展和局部化,同管道甩动实验观测极为符合。
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  softening region
The flow-stress curves are found to include both a work-hardening region and a work-softening region.
      
In both reinforced and unreinforced materials, the naturally aged conditions were cyclically unstable, exhibiting an initial hardening behavior followed by an extended region of cyclic stability and ultimately a softening region.
      
A Ludwig equation was modified to model the stress-strain behavior at a reference strain rate, which included elastic deformation, a yield-like peak, and a strain-softening region.
      
A softening moment-curvature relation is assumed for the beam and a closed form solution is obtained for a special kind of load, which shows that there exists a softening region in the beam and this region propagates along the beam.
      
In other instances, the studs could go into tension membrane after a well-defined softening region after the yield-buckling is achieved.
      
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Due to thstrain-softening of materials or due to the cross-sectional distortion of thin-walled beams in their large deflection,the moment-curvature relation of beams may display a hardening-softening characteristic.The recent work carried out by a research groupin Peking University has confirmed that when a semi-infinite beam with softening property is subjected to a suddenly applid constant velocity at its tip,softening may develop into asegment of finite length and travel along the beam. Meanwhile,in order...

Due to thstrain-softening of materials or due to the cross-sectional distortion of thin-walled beams in their large deflection,the moment-curvature relation of beams may display a hardening-softening characteristic.The recent work carried out by a research groupin Peking University has confirmed that when a semi-infinite beam with softening property is subjected to a suddenly applid constant velocity at its tip,softening may develop into asegment of finite length and travel along the beam. Meanwhile,in order to study pipe-whipphenomenon in nuclear plants,a research group in UMIST,UK,has made a thorough studyon the dvnamic behaviour of beams of finite length with hardening-softening characteris-tic. A theoretical model has been proposed to incorporate an elastic-hardening-softeningmoment-curvature relat ion into a large deflect ion dynamic analysis,and a correspondingfinite-difference programme has been developed.This theory can predict the initiation,de-velopment and localization of the softening region in the dynamically loaded beams,with avery good agreement with the experimental observation of pipe-whip tests.

由于材料的应变软化,或是由于薄壁梁在挠曲变形时的截面畸变,梁的弯矩一曲率关系可能呈现先强化后软化的性态。近几年来北京大学一个研究组的工作证实,具有软化特性的半无限长梁在自由端受常速度冲击时,软化可能发展为一个有限长的区段,并在梁内移动,同时,英国UMIST的一个研究组以核电站中的管道甩动问题为工程背景,集中研究了具有软化特性的有限长梁的动力行为。提出了计及弹性、强化、软化和梁的几何大变形的理论模型,并发展了相应的有限差分程序。这一理论模型能够预报软化区的萌生、发展和局部化,同管道甩动实验观测极为符合。

 
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