ארועים

JUMP CONDITIONS AND KINETIC RELATIONS AT MOVING DISCONTINUITIES IN SOLIDS

00:00 18-03-2009
<p class="MsoNormal" dir="ltr" style="DIRECTION: ltr; LINE-HEIGHT: 150%; unicode-bidi: embed; TEXT-ALIGN: left"><span style="FONT-SIZE: 12pt; LINE-HEIGHT: 150%"><font face="Arial, Helvetica, sans-serif"><font size="2">The problem of the kinetics of moving discontinuities is described on the example of the propagating phase-transition front that corresponds to </font></font></span></p> <p class="MsoNormal" dir="ltr" style="DIRECTION: ltr; LINE-HEIGHT: 150%; unicode-bidi: embed; TEXT-ALIGN: left"><span style="FONT-SIZE: 12pt; LINE-HEIGHT: 150%"><font face="Arial, Helvetica, sans-serif"><font size="2">a stress-induced martensitic phase transformation in an elastic bar. The representation of the martensitic volume fraction as an internal variable </font></font></span></p> <p class="MsoNormal" dir="ltr" style="DIRECTION: ltr; LINE-HEIGHT: 150%; unicode-bidi: embed; TEXT-ALIGN: left"><span style="FONT-SIZE: 12pt; LINE-HEIGHT: 150%"><font face="Arial, Helvetica, sans-serif"><font size="2">provides the explanation of the dissipation at the phase boundary in the framework of the canonical thermomechanics. </font></font></span></p> <p class="MsoNormal" dir="ltr" style="DIRECTION: ltr; LINE-HEIGHT: 150%; unicode-bidi: embed; TEXT-ALIGN: left"><span style="FONT-SIZE: 12pt; LINE-HEIGHT: 150%"><font face="Arial, Helvetica, sans-serif"><font size="2">The kinetic relation connecting the driving force at the discontinuity and its velocity is derived under the assumption of a linear dependence between </font></font></span></p> <p class="MsoNormal" dir="ltr" style="DIRECTION: ltr; LINE-HEIGHT: 150%; unicode-bidi: embed; TEXT-ALIGN: left"><span style="FONT-SIZE: 12pt; LINE-HEIGHT: 150%"><font face="Arial, Helvetica, sans-serif"><font size="2">the stress jump at the phase boundary and the driving force. The derived kinetic relation is consistent with jump relations at the discontinuity and </font></font></span></p> <p class="MsoNormal" dir="ltr" style="DIRECTION: ltr; LINE-HEIGHT: 150%; unicode-bidi: embed; TEXT-ALIGN: left"><span style="FONT-SIZE: 12pt; LINE-HEIGHT: 150%"><font face="Arial, Helvetica, sans-serif"><font size="2">satisfies limiting requirements. </font></font></span></p> <p class="MsoNormal" dir="ltr" style="DIRECTION: ltr; LINE-HEIGHT: 150%; unicode-bidi: embed; TEXT-ALIGN: left"><span style="FONT-SIZE: 12pt; LINE-HEIGHT: 150%"><font face="Arial, Helvetica, sans-serif"><font size="2">The comparison of the developed theory with available experimental data is made in the case of the dynamics of a straight brittle crack. </font></font></span></p> <p class="MsoNormal" dir="ltr" style="DIRECTION: ltr; LINE-HEIGHT: 150%; unicode-bidi: embed; TEXT-ALIGN: left"><span style="FONT-SIZE: 12pt; LINE-HEIGHT: 150%"><font face="Arial, Helvetica, sans-serif"><font size="2">The corresponding kinetic relation is derived under the same assumption as in the case of phase boundary. </font></font></span></p> <p class="MsoNormal" dir="ltr" style="DIRECTION: ltr; LINE-HEIGHT: 150%; unicode-bidi: embed; TEXT-ALIGN: left"><span style="FONT-SIZE: 12pt; LINE-HEIGHT: 150%"><font face="Arial, Helvetica, sans-serif"><font size="2">Classical results for Homalite-100 as well as recent experiments for Polyester/TiO<sub>2</sub> are compared with the prediction of the derived kinetic relation. </font></font></span></p> <p class="MsoNormal" dir="ltr" style="DIRECTION: ltr; LINE-HEIGHT: 150%; unicode-bidi: embed; TEXT-ALIGN: left"><span style="FONT-SIZE: 12pt; LINE-HEIGHT: 150%"><font face="Arial, Helvetica, sans-serif" size="2">The agreement between theory and experiment is rather good, especially for such a simple theoretical model.</font></span><b><i><font face="Tahoma" size="5"><span style="FONT-WEIGHT: bold; FONT-SIZE: 16pt; LINE-HEIGHT: 150%; FONT-STYLE: italic; FONT-FAMILY: Tahoma"></span></font></i></b></p><SPAN STYLE="display: none"> <P>Acetylenide minutes, pointedly? 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