PSI - Issue 2_B

L. Chang et al. / Procedia Structural Integrity 2 (2016) 309–315 J.G. Williams / Structural Integrity Procedia 00 (2016) 000 – 000

311

3





h h c

c h

h

sin sin 

 

sin



, i.e.

, and

(1)





tan







  

h h c



sin

sin





cos





Thus φ may be determined directly from the chip thickness to cut depth ratio. For the crack tip touching condition, the external work available for energy dissipation is (F c /b-G c ) dx, where dx is the tool movement. The shear force on the tool face is   sin cos b F G b F b S t c c        and the displacement along the tool face is dx c and  

dx

h

sin



 

c



  

dx

h

sin



c

The friction energy dissipation is thus,

  

  

b F    

b F t

sin



  

 (2) Using the Tresca yield criterion, t he shear stress on the shear plane is taken as σ Y /2 giving a shear force on the plane of σ Y h/2sinφ , and the shear displacement is   dx du s      sin sin The energy dissipated in shear is,   h dx dx h h du Y Y s Y               2 sin sin sin 2 2sin (3) where γ is the shear strain :          sin sin sin The energy dissipation in plastic bending may be found by measuring the residual radius of curvature of the chip, R, which gives rise to a bending strain of e b =h c /2R. The plastic bending term is thus given approximately by, dx h h e h dx R h dx b R M c b Y Y c p      ) ( 2 1 4 1 2   (4) Thus from equations 1 – 4 we have     dx h dx h e h dx h b F G b G dx F b F c b Y Y t c c c c                      ) ( 2 sin sin sin 2 sin sin sin cos            (5) This is the equation used in method 2 in [1] and enables G c and σ Y to be found by measuring h, and in this case h c also. Here the additional term (e b /γ)(h c /h) is included. This form includes the friction energy and no assumptions as to friction laws need be made in determining G c and σ Y .  dx    G c c     sin sin cos        and hence c c h h e h         1 b Y t b F c G b F                     tan 1 tan 2 tan

3. Materials Data

The materials used in the analysis include polyethylene of different molecular weights, ranging from 0.5 to 70 million g/mol, denoted as high density polyethylene (HDPE), high molecular weight polyethylene (HMWPE) and ultra-high molecular weight polyethylene (UHMWPE); polypropylene (PP), polyether ether ketone (PEEK), neat epoxy (EPOXY) and carboxyl-terminated butadiene-acrylonitrile (CTBN) rubber modified epoxy (EPOXY/RUBBER). Simple compression test was carried out for the materials. The tests were performed on