1 Natural Strain Near Welding Interface For Different Collision Angles EPNM-2008 Lisse, Netherlands H.H. Yan; X.J. Li May 6-9, 2008 Dalian University of Technology

2 Outline of talk Introduction Model Solutions Results Discussions

3 Introduction Where will strain rate and strain be used? To analyze the acting of mechanics and thermodynamics To setup the model of heat transmission To estimate the thickness of layer melted And so on Temperature ? For example: Base plate Flyer plate

4 Temperature? Caused by Shock compaction Caused by deformation energy Strain rate? Strain? To research here

5 Model Ideal fluid Symmetrical collision 1

6 Reason of adopting the model Detonation of explosive is about 2000~3000 m/s. Pressure (1.6~3.5) × Pa Strength of materials >10 negligible So compressibility small + <6% Ideal Liquid model

7 Transforming holographic function method 2 Boundary condition:

8 Solutions (Strain) Strain rate Strain X Horizontal ordinate Y Vertical ordinate u Horizontal velocity v Vertical velocity Eddy factor considered Along stream line Points on the line Steady assumption Incompressiblity conservation of momentum model holographic function method finite difference method

9 solving x,y,u,v The complex potential velocity potential stream function XyuvXyuv solved For stream line given With u,v changing

10 Stream lines plotted Fig. Different flow diagrams with different ψ at β=13 0 Y( H 2 /2 ) X(H 2 /2)  ~ ＝ 0.5  ~ ＝ 0  ~ ＝ -  ~ ＝ -1  ~ ＝ -2 3

11 Solving stain rate (along stream line) incompressibe irrotational solved second-order tensor

12 Strain rate results (For example) 4 5 4

13 Results of strain rate For the same relative streamline, at the points with the same relative horizontal ordinate, calculations showed that the ratio of tensile and shear strain rate to the stagnation point strain rate is very similar for colliding angles in the range 6–20º. in detail:( the paper) H.H. Yan, X.J. Li. Strain rate distribution near welding interface for different collision angles in explosiveWelding International Journal of Impact and Engineering.2008 ， 35 ： 3-9.

14 Solving stain (along stream line) When the continuums deform, displacement, eddy and distortion of each infinitesimal among them will change. Its orientation and shape will change at any time. According to the steady assumption, the streamline is same as the trace; that is to say, change of strain along the streamline is same as that along the trace. To calculate the strain distribution, the eddy factor must be eliminated. 6

15 Calculating Process ： + + To calculate the natural strain by eliminating the eddy factor In detail Transformation relation

16 Strain results (For example) 5 7 8

17 Discussion The model adopted is simple and ideal If the viscous-elastic constitutive equations were used to analyze stain field, explosive welding mechanics will be explained very well. If the geometric non-linearity was considered, the Green’s and Almansi’s strain can be used in the future.

18 THANK YOU