EBK MANUFACTURING PROCESSES FOR ENGINEE
EBK MANUFACTURING PROCESSES FOR ENGINEE
6th Edition
ISBN: 9780134425115
Author: Schmid
Publisher: YUZU
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Chapter 6, Problem 6.130P
To determine

Theexpression for wires drawing stress σd in plane strain drawing of a flat sheet.

Expert Solution & Answer
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Answer to Problem 6.130P

The expression for wires drawing stress σd in plane strain drawing of a flat sheet is σd=Sy(1+tanαμ)[1( hf h 0 )μcotα] .

Explanation of Solution

Formula used:

The expression flow stress is given as,

  Y'=σmaxσmin ...... (1)

Here, σmax is the maximum stress generated and σmin is the minimum stress generated.

Calculation:

The figure (1) shows the force analysis during the extrusion process,

  EBK MANUFACTURING PROCESSES FOR ENGINEE, Chapter 6, Problem 6.130P

Figure (1)

Here, p is the pressure applied by the rollers, μp is the frictional force, σx is the tensile force, h0 is the initial force and hf is the final force and w is the width of the specimen.

Evaluate the forces in the x-direction,

  (σx+dσx)(h+dh)wσxhw+pwdxcosα+μpdxcosα=0hwσx+hwdσx+dhwσx+d2hwσxσxhw+pwdxcosα+μpdxcosα=0hwdσx+dhwσx+d2hwσx+pwdxcosα+μpdxcosα=0

Ignoring the second order terms in the above equation and divide whole equation by w .Therefore,

  hdσx+dhσx+p(1+μtanα)dh=0 ...... (2)

Since positive pressure is indicated by negative stress,

  σmaxσmin=σx+p

From equation (1),

  Y'=σx+pp=Y'σx ....... (3)

By equation (2) and (3),

  hdσx+dhσx+(Y'σx)(1+μ tanα)dh=0hdσx+dhσx+(Y'( 1+ μ tanα )dhσx( 1+ μ tanα )dh)=0hdσx+dhσx+(Y'( 1+μcotα)dhσx( 1+μcotα)dh)=0hdσxσxdh[1(1+μcotα)]+Y'(1+μcotα)dh=0

On further solving,

  hdσxσxdhμcotα+Y'(1+μcotα)dh=0hdσx=dh[σxμcotα+Y'(1+μcotα)]dhh=dσxσxμcotαY'( 1+μcotα)

Boundary conditions are as follows,

At h=h0 , σx=σd and also at h=hf , σx=0 .

Integrating both sides in the limits,

   h 0 h f dhh= σ d 0 d σ x σ x μcotαY'( 1+μcotα ) σd=Y'(1+μcotαμcotα)[1( h f h 0 )μcotα]σd=Y'(1+tanαμ)[1( h f h 0 )μcotα]

Conclusions:

Therefore, the expression for wires drawing stress σd in plane strain drawing of a flat sheet is σd=Sy(1+tanαμ)[1( hf h 0 )μcotα] .

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Chapter 6 Solutions

EBK MANUFACTURING PROCESSES FOR ENGINEE

Ch. 6 - Prob. 6.11QCh. 6 - Prob. 6.12QCh. 6 - Prob. 6.13QCh. 6 - Prob. 6.14QCh. 6 - Prob. 6.15QCh. 6 - Prob. 6.16QCh. 6 - Prob. 6.17QCh. 6 - Prob. 6.18QCh. 6 - Prob. 6.19QCh. 6 - Prob. 6.20QCh. 6 - Prob. 6.21QCh. 6 - Prob. 6.22QCh. 6 - Prob. 6.23QCh. 6 - Prob. 6.24QCh. 6 - Prob. 6.25QCh. 6 - Prob. 6.26QCh. 6 - Prob. 6.27QCh. 6 - Prob. 6.28QCh. 6 - Prob. 6.29QCh. 6 - Prob. 6.30QCh. 6 - Prob. 6.31QCh. 6 - Prob. 6.32QCh. 6 - Prob. 6.33QCh. 6 - Prob. 6.34QCh. 6 - Prob. 6.35QCh. 6 - Prob. 6.36QCh. 6 - Prob. 6.37QCh. 6 - Prob. 6.38QCh. 6 - Prob. 6.39QCh. 6 - Prob. 6.40QCh. 6 - Prob. 6.41QCh. 6 - Prob. 6.42QCh. 6 - Prob. 6.43QCh. 6 - Prob. 6.44QCh. 6 - Prob. 6.45QCh. 6 - Prob. 6.46QCh. 6 - Prob. 6.47QCh. 6 - Prob. 6.48QCh. 6 - Prob. 6.49QCh. 6 - Prob. 6.50QCh. 6 - Prob. 6.51QCh. 6 - Prob. 6.52QCh. 6 - Prob. 6.53QCh. 6 - Prob. 6.54QCh. 6 - Prob. 6.55QCh. 6 - Prob. 6.56QCh. 6 - Prob. 6.57QCh. 6 - Prob. 6.58QCh. 6 - Prob. 6.59QCh. 6 - Prob. 6.60QCh. 6 - Prob. 6.61QCh. 6 - Prob. 6.62QCh. 6 - Prob. 6.63QCh. 6 - Prob. 6.64QCh. 6 - Prob. 6.65QCh. 6 - Prob. 6.66QCh. 6 - Prob. 6.67QCh. 6 - Prob. 6.68QCh. 6 - Prob. 6.69QCh. 6 - Prob. 6.70QCh. 6 - Prob. 6.71QCh. 6 - Prob. 6.72QCh. 6 - Prob. 6.73PCh. 6 - Prob. 6.74PCh. 6 - Prob. 6.75PCh. 6 - Prob. 6.76PCh. 6 - Prob. 6.77PCh. 6 - Prob. 6.78PCh. 6 - Prob. 6.79PCh. 6 - Prob. 6.80PCh. 6 - Prob. 6.81PCh. 6 - Prob. 6.82PCh. 6 - Prob. 6.83PCh. 6 - Prob. 6.84PCh. 6 - Prob. 6.85PCh. 6 - Prob. 6.86PCh. 6 - Prob. 6.87PCh. 6 - Prob. 6.88PCh. 6 - Prob. 6.89PCh. 6 - Prob. 6.90PCh. 6 - Prob. 6.91PCh. 6 - Prob. 6.92PCh. 6 - Prob. 6.93PCh. 6 - Prob. 6.94PCh. 6 - Prob. 6.95PCh. 6 - Prob. 6.96PCh. 6 - Prob. 6.97PCh. 6 - Prob. 6.98PCh. 6 - Prob. 6.99PCh. 6 - Prob. 6.100PCh. 6 - Prob. 6.101PCh. 6 - Prob. 6.102PCh. 6 - Prob. 6.103PCh. 6 - Prob. 6.104PCh. 6 - Prob. 6.105PCh. 6 - Prob. 6.106PCh. 6 - Prob. 6.107PCh. 6 - Prob. 6.108PCh. 6 - Prob. 6.109PCh. 6 - Prob. 6.110PCh. 6 - Prob. 6.111PCh. 6 - Prob. 6.112PCh. 6 - Prob. 6.113PCh. 6 - Prob. 6.114PCh. 6 - Prob. 6.115PCh. 6 - Prob. 6.116PCh. 6 - Prob. 6.117PCh. 6 - Prob. 6.118PCh. 6 - Prob. 6.119PCh. 6 - Prob. 6.120PCh. 6 - Prob. 6.121PCh. 6 - Prob. 6.122PCh. 6 - Prob. 6.123PCh. 6 - Prob. 6.124PCh. 6 - Prob. 6.125PCh. 6 - Prob. 6.126PCh. 6 - Prob. 6.127PCh. 6 - Prob. 6.128PCh. 6 - Prob. 6.129PCh. 6 - Prob. 6.130PCh. 6 - Prob. 6.131PCh. 6 - Prob. 6.132PCh. 6 - Prob. 6.133PCh. 6 - Prob. 6.134PCh. 6 - Prob. 6.135PCh. 6 - Prob. 6.136PCh. 6 - Prob. 6.137PCh. 6 - Prob. 6.138PCh. 6 - Prob. 6.139PCh. 6 - Prob. 6.140PCh. 6 - Prob. 6.142DCh. 6 - Prob. 6.143DCh. 6 - Prob. 6.144DCh. 6 - Prob. 6.145DCh. 6 - Prob. 6.146DCh. 6 - Prob. 6.147DCh. 6 - Prob. 6.149D
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