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HEAT GENERATION IN PLASTIC DEFORMATION

USING ANSYS® MECHANICAL APDL AND

WORKBENCH V14.5: APPLICATION OF THE NEW

ACT MODULE

Figure 1: Temperature in a Steel Bar Stretched with Plastic Deformation

ANSYS Mechanical APDL has multiphysics element types that can use displacement

and temperature degrees of freedom at their nodes, support nonlinear structural andthermal material properties, and predict the heat generated by plastic work converted

to heat. This permits modeling of thermoplastic heat generation with ANSYS

Multiphysics and with ANSYS Mechanical licenses.

This article uses the SOLID226 20-node brick high order element in such an

application. Note the importance of the correct units for Specific Heat, Thermal

Conductivity and Thermal Loads in models of this type.





Selection of an Element to Support Thermoplastic Heat Generation

Three ANSYS elements support the thermoplastic effect, “which manifests itself as an

increase in temperature during plastic deformation due to the conversion of some of

the plastic work into heat” (Theory Reference, 11. Coupling, 11.3. Thermoplasticity).

Thermoplastic analysis exists in the following ANSYS elements:

PLANE223 - 2-D 8-Node Coupled-Field Solid

SOLID226 - 3-D 20-Node Coupled-Field Solid

SOLID227 - 3-D 10-Node Coupled-Field Solid

Setting KEYOPT(1) to 11 activates displacement and temperature degrees of

freedom for these elements.

During direct coupled analysis, structural-thermal coupling can have Strong (matrix)

coupling which produces an unsymmetric matrix, or Weak (load vector) coupling

which produces a symmetric matrix and requires at least two iterations per substep.

Coupling choice is set with KEYOPT(2). As quoted below, Weak coupling is

recommended in static and transient analysis. The Coupled-Field Analysis

Guide, 2. Direct Coupled-Field Analysis mentions Strong coupling if contact elements

are used. Note the following comments:

“Because of the possible extreme nonlinear behavior of weakly coupled field elements,

you may need to use the predictor and line search options to achieve convergence.”

“To speed up convergence in a coupled-field transient analysis, you can disable the

time integration effects for any DOFs that are not a concern. For example, if

structural inertial and damping effects can be ignored in a thermal-structural

transient analysis, you can issue TIMINT,OFF,STRUC to turn off the time integration

effects for the structural degrees of freedom.”

In the Coupled-Field Analysis Guide, 2. Direct Coupled-Field Analysis, 2.6.

Structural-Thermal Analysis it states:

“In a structural-thermal analysis with structural nonlinearities using elementsPLANE223, SOLID226, and SOLID227, it is recommended that you use weak (load





vector) coupling between the structural and thermal degrees of freedom (KEYOPT(2)

= 1) and suppress the thermoelastic damping in a transient analysis (KEYOPT(9) = 1).

When using the SOLID226 element, you should also select the uniform reduced

integration option (KEYOPT(6) = 1). These options will be automatically set if

ETCONTROL is active.

“PLANE223, SOLID226, and SOLID227 also support a thermoplastic effect

calculation in static or transient analyses. For more information, see Thermoplasticity

in the Mechanical APDL Theory Reference.”

In the present example, the above recommendations have been considered.

Figure 2: The SOLID226 20-Node Brick Coupled Element

In more general 3D meshing, users will want to consider the use of both the

SOLID226 and SOLID227 elements for this sort of coupled analysis.

For further reading, users can consult: Theory Reference, 11. Coupling, 11.3.

Thermoplasticity

Materials for Thermoplastic Heat Generation

In addition to the usual thermal and structural material properties, elements that

capture Thermoplastic Heat Generation will require the Taylor-Quinney coefficient

(input as QRATE on the MP command) which is the decimal fraction of plastic work

that is converted to heat, and a model of material plasticity, such as Isotropic or





Kinematic Hardening. Typical QRATE values might fall in the range of between 0.80

and 0.95, however, users will be responsible for finding values that are appropriate

for the materials being studied. Required material properties will include MP

commands for structural and thermal behavior. An example in SI units for a fictitious

steel material is:

Youngs Modulus of Elasticity EX=0.2070000E+12 MPa

Poisson’s Ratio NUXY=0.2900000

Coefficient of Thermal Expansion ALPX=0.1510000E-04

Density DENS=7850.000 kg/m3

Thermal Conductivity KXX=46.70000 W/m/C

Specific Heat C=419.0000 W/kg/CTaylor-Quinney Coefficient QRATE=0.9000000

Heating due to plastic deformation will require a material plasticity model input with

TB commands. A simple example in SI units is a Bilinear Isotropic Hardening model

with:

Yield Stress 1.0e8 MPaTangent Modulus 1.0e9 MPa

If heat is to be produced, loading high enough to cause yielding and plastic

deformation will be required.

UNITS in the Model

Proper use of Units in the model must be emphasized. Thermal loads must be in

appropriate energy units. Plastic strain energy will be in the units of Force !

Distance. Material properties for Thermal Conductivity and Specific Heat must

contain energy expressed in the form of this physical work, not units such as BTUs

in US Customary units. It is simplest to do everything in SI units, as employed

in the present example. Note the units of Watts (Joules per second, i.e. Newton-

Meters per second) above.

Users desiring to work in units such as inches or millimeters must represent Thermal

Conductivity and Specific Heat in energy units in inch-pounds for the inches





system, or millimeter-Newtons for the millimeters system, respectively. This type of

conversion is hidden from the user but is employed internally when Workbench

Mechanical is chosen for thermal analysis.

Loading on the ModelThe model has symmetry constraints on the back, left, and bottom sides. The right-

hand side has a non-zero displacement in the +X direction—enough to cause 10%

total strain in the model X direction. The solution has been set up to ramp up the

non-zero displacement through many Substeps in one Load Step.

Figure 3: Displacement Constraints

The model has a convective heat transfer surface load on the top and front sides. Inthe following Figure 4, grey arrows show where the convective load is applied. The

arrows are grey because a Table Array that is a function of Time is used to apply a

constant convective load that does not vary over time during substeps.





Figure 4: Convection Thermal Loading

Some users consider adiabatic loading, with the assumption that the deformation

event is so rapid that there is no significant conduction of heat. This can be mimicked

in ANSYS with a short time interval. The adiabatic effect can also be suggested if

thermal loads are removed, and a near-zero thermal conductivity is entered. Users

need to consider whether near zero thermal conductivity creates thermal transient

analysis difficulties.

The convection coefficient was applied with the Table Array “H_CONV” which was

set to hold a constant value over time, as can be seen below in Figure 5:





Figure 5: Convective Coefficient via Table Array

Element Choice and KEYOPT Settings

In this example, a solid rectangle has been meshed with a mapped mesh of SOLID226

elements. The SOLID226 element options are shown in Figure 6 below.

Figure 6: SOLID226 Element Options for Thermoplastic Heat Generation

Note the Weak (load vector) coupling (contact not used here), and Reduced





Integration settings.

Solution Controls

Large displacement transient analysis has been applied with many substeps. For the

purpose of the present test, tightened convergence controls were employed, although

such tight settings may not be required in some user models. The model has been

simplified by the use of material properties that are not temperature dependent.

It is usually important that the structural analysis transient be suppressed. The

following two commands can set the thermal transient analysis ON, and the

structural transient analysis OFF in the time integration that is performed in this

example:

TIMINT,ON,THERMTIMINT,OFF,STRUCT

Some of the settings for the current example are shown in the Solution Controls

dialog box in Figure 7:





Figure 7: Example Settings for Large Displacement Transient Analysis

In addition to the above, loading was set to “Ramped” so that the applied non-zero

displacement loading in this model is ramped up through the substeps of the load

step. Because of the load ramping, the Table Array of Figure 5 was used to hold

constant the convection coefficient load over all substeps.

Outputs from the Example Model

The input material property QRATE for the Taylor-Quinney coefficient was 0.9 in

this example, so 90% of the plastic strain energy is converted into heat. The specific

heat C and the density DENS are set to values typical of a steel material. One of the

available outputs with ANSYS materials with kinematic and isotropic hardening isthe plastic work per unit volume, PLWK, as plotted for example with

PLESOL,NL,PLWK.

A simplified check on a resulting temperature in an adiabatic analysis is to calculate

local temperature change with the temperature change calculation:

Delta_T = QRATE*PLWK/C/DENS

Typical values for strains of a few percent in steel produce a temperature change of

only a few degrees, which is why this effect is often ignored in structural analysis.

More extreme temperature changes may occur during cyclic loading, high-speed

metal forming, extrusion, and events better suited to explicit dynamic analysis.

In the present example, the above calculation produced Delta_T of 3.803 degrees.

The model started with an initial temperature of 22 degrees, and the resulting peak

temperature after a 10% strain was 25.738 degrees—a slightly smaller 3.738 degree

temperature change than hand calculated because of convective cooling in the model

and because of approximations introduced by element behavior, mesh density and

transient integration.





Figure 8: Resulting Temperature Profile

Because the SOLID226 element is a coupled element, deflections, stresses and strains

can also be immediately plotted and listed.

A Workbench Mechanical Approach with ACT

Since the early days of ANSYS WorkBench Mechanical, it has been possible to insert

APDL Command Objects (snippet commands) to modify a structural model.

Depending on the location of the snippet commands, one would access differentproperties of the Finite Element Model and would be able to change it. It was a very

efficient way to combine the best of both Mechanical and Mechanical APDL worlds:

the power of APDL commands within the user-friendly efficient WorkBench platform.

The main drawbacks of this method were that user would have to be very careful with

the units, and consistent between the writing of the APDL commands and the

definition of the Mechanical model, especially with the Named Selections. To make

long story short, it was error prone and not efficient to be deployed across the





company.

With R14.5, ANSYS has developed the Application Customization Toolkit that enables

you to fill the gap between the Mechanical APDL features and their exposure in

Mechanical: it is a great improvement that will enable the old snippet commands orold legacy APDL macros to be embedded in custom Mechanical objects that inherits

the behavior of standard WorkBench objects. ACT provides you with APIs manipulate

a wide range of data (geometry, finite element, material) to change the APDL code

which is written when one clicks on the solve button.

Figure 9 : Dedicated Mechanical Toolbar created with ACT.

For instance, taking into account heat generation in plastic deformation would

require changing the default element type created by the standard interface and

adding the desired material property QRATE: it would convert the SOLID186/187

elements into coupled SOLID226/227 elements with the desired keyoptions:

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Heat Generation in Plastic Deformation using ANSYS® Mechanical APDL and Workbench v14.5: application of the new ACT module | FEA | Tips and Tricks | Newsletters