Introduction:

When designing mechanical systems, a lot of attention is given to the materials used since they should withstand high temperatures, constant dynamic motion, and other stresses. While materials were earlier tested under extreme conditions, today the scenario runs differently. Materials are first tested computationally before prototypes are used.

In accordance with a previous project that we published (titled – Understanding the failure behavior of a plate), we decided to work on a similar project where we compared the failure behavior between three materials and understand how each material reacts during collision.

Objective:

The objective of this project is to analyze and compare the failure behavior of the plate. We used two materials in this project – Law 1, Law 36, and Law 27. Upon simulating collision, we studied how the materials fail under stress.

Model setup:

Before we proceeded with the simulation, we set up the punch and the plate. The punch is designed with a mass of 5gms. It is made to impact the plate by defining an Imposed Velocity card. The Imposed Velocity refers to the velocity with which the punch moves towards the plate.

Punch and plate setup

Imposed Velocity Card

Material Property of Law-1:

In this case, the plate is defined with a LAW-1 material which defines the basic properties of elastic material. This model considers only the elastic phase of the material, there is no plasticity involved which results in linear deformation. The material has density, Young’s Modulus, and Poisson’s ratio.

Observation:

  • During the simulation, the plate displays perfect elasticity with no plastic strain. It stretches completely when the load is applied and returns to its original shape when the load is removed.

  • When deformation or cracking occurs, some energy is lost. During the simulation of such behavior, this energy is not captured properly. Hence, there is a difference between the energy levels of the system before and after deformation. This energy that is not captured is called Hourglass Energy. When performing simulations, our objective is to keep this Hourglass Energy to minimum levels. The Hourglass energy in this scenario remains zero because the physical stabilization of Hourglass Energy is achieved through element formulation.
  • We will also define contact between the two surfaces. This contact is created between the master and slave nodes. When the two surfaces come into close contact, the contact energy will act to simulate deformation. If we do not define contact, the two surfaces will penetrate each other. In this project, the contact energy levels remain at zero.
  • The internal energy of the plate increases linearly due to the absorption of the kinetic energy from the impacting sphere and drops down once the plate returns to the original shape.

  • The kinetic energy gradually increases as the plate is stretched to the maximum limit for the applied load.

Material Property of Law-36:

The material we will be testing is LAW – 36. This material medium defines the basic properties of a plastic material. This material card uses the True stress-strain curve function by the user to define the hardening portion of the curve.

The failure criteria in this material card are,

Eps_max = 0.16 (Failure Plastic strain)

EPS_t = 0.1 (Tensile failure strain where the stress starts to reduce)

EPS_m = 0.11 (Maximum failure strain, where the element strain is set to zero)

Material card:

Curve data:

Observation:

  • There is a gradual deletion of elements as the plastic strain in the elements reaches 0.16. This deletion refers to the elements failing as the strain increases.

  • The Internal Energy of the plate increases linearly since the Kinetic Energy from sphere is transferred to it through the impact between them.
  • When deformation or cracking occurs, some energy is lost. When simulating such behavior, this energy is not captured properly. Hence, there is a difference between the energy levels of the system before and after deformation. This energy that is not captured is called Hourglass Energy. When performing simulations, our objective is to keep this Hourglass Energy to minimum levels. The Hourglass Energy in this scenario remains zero because of the physical stabilization of the Hourglass Energy is achieved through the element formulation.
  • We also define contact between the two surfaces. This contact is created between the master and slave nodes. When the two surfaces come into close contact, the contact energy will act to simulate deformation. If we do not define contact, the two surfaces will penetrate each other. In our project, the contact energy levels remain at zero.

  • There is no noise present in the graph which you can see in the spike in the Kinetic Energy curve because the elements are deleted together.

Material Property of Law-27:

The material we will be testing is LAW – 27. This material model is like the Johnson-Cook material model along with the brittle failure card. This card is used for modeling brittle materials.

Material card:

The failure criteria are given in the material card are,

EPS_t1= EPS_t2= 0.14(the tensile failure strain starts reducing)

EPS_m1= EPS_m2= 0.15(the tensile failure strain reaches zero)

EPS_f1= EPS_f2= 0.151(the plastic strain at which the elements get deleted)

Damage factor (Dmax) = 0.999

Observations:

  • The elements start to fail when the EPS_f value reaches one integration point. There is a slight elasticity seen in the plate before the failure takes place.

  • The Hourglass Energy and the Contact energy remains zero because of the Physical stabilization of the hourglass.
  • The Internal Energy of the plate increases linearly due to the absorption of the Kinetic Energy from the impacting sphere.

  • Since the elements are getting deleted there is a noise in the graph. Towards the end of the curve, there is a sudden hike due to the deletion of a big chunk of an element.

Conclusion:

The best case for on-field scenario totally depends upon the scenario, i.e, if the brittle material must be studied then Law-27 is the best, whereas, to study an elastic material Law-1 would be suitable. We can employ the same procedure to analyze the failure behavior of other materials such as elastoplastic, elastic material, etc. and decide the best material for a piece of equipment.


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