COMPARISON OF DIFFERENT MATERIAL LAWS IN RADIOS

Aim

To compare johnson cook material material curve with platic material curve for a rupture plate and anlyze the results 

 

Solution

We will be discussing about the material models which are used to analyse the given components and find their failure models :

 

 

Elastic region :

The elastic region is the portion of the curve where the material will return to its original shape if the load is removed.

Yield point:The yield point is the point on a stress-strain curve that indicates the limit of elastic behavior and the beginning of plastic behavior. Prior to the yield point, a material will deform elastically and will return to its original shape when the applied stress is removed.

 

Plastic Region:

Plasticity describes the deformation of a (solid) material undergoing non-reversible changes of shape in response to applied forces. For example, a solid piece of metal being bent or pounded into a new shape displays plasticity as permanent changes occur within the material itself.

 

Ultimate tensile strength  :The ultimate tensile strength (UTS) is a material\'s maximum resistance to fracture. It is equivalent to the maximum load that can be carried by one square inch of cross-sectional area when the load is applied as simple tension.

 

Now in hypermesh few material laws are defined which help in the analysis of the various kinds of materials which either are elastic or plastic.These are :

 

1.Law 1 : For purely elastic 

2.Law 2 : For alloys such as steel

3.Law 27 : Elastic - Brittle materials

4.Law 36 : Elastic - plastic

5.Law 42 : Hyperelastic

6.Law 70: Foam

 

1.Law 1 : Elastic Materials 

Law 1 is mostly used for elastic materials and is not used in simulations as it does not consider the large deformations .

 

2.Law 2 : John plastic Materials 

This law takes account the large plastic deformations produced in the alloys such as steel.It is used only for shell elements.

 

3.Law 36 : Elastic Plastic Piecewise linear material 

This law models an isotropic material using user defined functions for the work the work hardening portion of the stress strain curve for different strain rates .It gives the advantage of better results .It takes account of the strain rate curve obtained from lab curve.It can be used for all types of elements.

 

 

 

Now we will be doing impact analysis of the following component with various laws and compare parameter of the different results :

 

 

 

Case 1 : LAW 2 : JOHN PLAST MATERIAL WITH JOHNSON FAILURE  METHOD WITH XFEM=0

 

We will simulate the file and check for energy error :

 

 

As you can see energy error is less than -15 % and not more than 5% hence the energy of the system is mostly conserved and hence we go ahead check the results of various parameters .

 

a.Total cycles : 49480

   Elapsed Time : 106 s

   Energy error : Maximum : 1 % and minimum : -.3 %

   Mass error : 0 % 

 

b.Element failure :

As we have not applied XFEM=1 ,the elements are getting deleted instead of a crack propagation as shown below :

As you can see the elements are getting deleted and ball starts going into the  plate as shown.

 

As you can see the elements are deleted and the stress in the region has fallen to the minimum and the ball has gone full through the plate at the end of the simulation.

 

c.Results for various parameters :

 

 

 

 

 

 

Case 2 : LAW 2 : JOHN PLAST MATERIAL WITH JOHNSON FAILURE  METHOD WITH XFEM=1

 

a.Total cycles : 49397

   Elapsed Time : 112 s

   Energy error : Maximum : 3.8 % and minimum : -.3 %

   Mass error : 0 % 

 

b.Element failure :

 

 

 

c.Results for various parameters :

 

 

 

 

 

 

Case 3 :JOHN PLAST MATERIAL WITHOUT JOHNSON FAILURE  METHOD 

 

a.Total cycles : 49405

   Elapsed Time : 106 s

   Energy error : Maximum : 1 % and minimum : -.3 %

   Mass error : 0 % 

 

b.Element failure :

 

 

 

c.Results for various parameters :

 

 

 

 

 

 

 

 

Case 4 :JOHN PLAST MATERIAL WITH  EPS MAX = 0

 

a.Total cycles : 43904

   Elapsed Time : 128 s

   Energy error : Maximum : 1 % and minimum : -.3 %

   Mass error : 0 % 

 

b.Element failure :

 

 

 

 

 

c.Results for various parameters :

 

 

 

 

Case 5 : LAW 1 WITH SAME DENSITY

 

a.Total cycles : 47969

   Elapsed Time : 112 s

   Energy error : Maximum : 1 % and minimum : -.3 %

   Mass error : 0

 

b.Element failure :

 

 

 

c.Results for various parameters :

 

 

 

 

 

 

 

 

 

 

Case 6 : LAW 36 WITH RECOMMENDED PROPERTIES 

 

Now we will introduce the test curve as shown below:

 

 

 

 

Recommended properties :

 

 

 

a.Total cycles : 16152

   Elapsed Time : 395 s

   Energy error : Maximum : 1 % and minimum : -.3 %

   Mass error : 0

 

b.Element Failure 

 

 

 

 

c.Results for various parameters :

 

 

 

 

 

Case 7 : LAW 27

 

a.Total cycles : 49450

   Elapsed Time : 107 s

   Energy error : Maximum : 1 % and minimum : -.3 %

   Mass error : 0 % 

 

 

b.Element Failure:

 

 

 

 

 

c.Results for various parameters :

 

 

 

 

 

Conclusion:

 

Case1:

In case 1 we have applied john plastic material law with johnson failure with xfem=0 ,hence no crack propagation takes place and the elements get deleted .This law does not take account the temperature changes and the strain rate and hence is not fully accurate .

 

Case2:

In case 2 we have applied john plastic material law with johnson failure law with xfem=1,hence the crack propagation takes place but the stresses are so high at a few places that the it exceeds the maximum displacment allowed and the elements get deleted at the center .The law does not take account of the temperature changes and the strain rate and hence is not fully accurate .

 

Case3:

In case 3 we have not applied the johnson failure method as shown and the stresses produced are higher and the plates elements are thrown off due to the impact.

 

Case4:

In case 4 we have applied john plastic material law with johnson failure law with xfem=0,hence the crack propagation takes place but the stresses are so high at a few places that the it exceeds the maximum displacment allowed and the elements get deleted at the center .The law does not take account of the temperature changes and the strain rate and hence is not fully accurate .

 

Case5:

In case 5 we have applied law 1 which assumes that the material only has elastic region and no plastic region and hence no deformation takes place and the elements are not deleted or no crack propagation takes place .This law is not widely used as it does not represent the realilty.

 

Case6:

Law 36 is the most accurate law which takes account of the lab strain rate and hence gives more accurate results .

 

Case7:

This is law 27 which takes account  of the plastic brittle materials going deformation and we can see that the plate ruptures as it is a brittle material and cannot take account of any deformation .

 

 

Hence we conclude that we should use law 36 with john failure method as it takes account of the tested lab strain rate .