Composite Impact

Modeling Composite Material Impact with Abaqus/ExplicitLecture 13

L13.*Analysis of Composite Materials with Abaqus

OverviewIntroductionComposite Damage Models in Abaqus/ExplicitUnidirectional FiberExample Composite Plate ImpactWoven FabricExample Corrugated Beam CrushingModeling Techniques

Introduction


IntroductionImpact resistance of composite materials is of primary importance in many industries AutomotiveRoad debrisVehicle crashworthinessAerospaceAircraft crashworthinessBird strikeDefenseBallistics

Composite Damage Models in Abaqus/Explicit


Composite Damage Models in Abaqus/ExplicitAbaqus/Explicit provides additional damage models for fiber-reinforced composite materials.The built-in damage model discussed in Lecture 9 can only be used with elements that have a plane stress formulation.Plane stress, membrane, and shell elements. User-defined material subroutines (VUMATs) are available to extend this capability to elements with other stress states (3D, for example).Composite damage VUMATs Two routines are available:Unidirectional fiber VUMAT (extension of built-in capability to include 3D)Available via SIMULIA Answer 3123Woven fabric VUMATAvailable as a built-in user subroutineBoth of these routines require user input to specify how the composite materials will behave under load.

Unidirectional Fiber VUMAT


Unidirectional Fiber VUMATThe primary assumption is that elastic stress/strain relations are given by orthotropic damaged elasticity

Four damage variables are introducedTwo associated with fiber tension and compression

Two associated with matrix tension and compression


Unidirectional Fiber VUMATThese four damage variables are used to define global fiber and matrix damage variables.

The damaged elastic constants, Cij, are defined in terms of the undamaged elastic constants and the damage variables.

The factors smt and smc control the loss of shear stiffness by matrix tensile and compressive failure, respectively.


Unidirectional Fiber VUMATThe undamaged elastic constants are functions of the undamaged Youngs moduli and Poissons ratios


Unidirectional Fiber VUMAT19 user material constants must be specified for this subroutineYoungs moduli in the three primary axesE011, E022, E033Poissons ratios n12, n13, n23Shear moduli G012, G013, G023Shear strengths S12, S13, S23Tensile and compressive failure stress in each primary directionX1t, X1c, X2t, X2c, X3t, X3c Damping (optional) b


Unidirectional Fiber VUMATData input*MATERIAL, NAME=matName*DENSITY r*USER MATERIAL, CONSTANTS=27

*DEPVAR, DELETE=5 17Why did the previous slide indicate 19 constants are required?


Unidirectional Fiber VUMATOutputIn addition to the standard output variables for stress-displacement elements, the following output variables have a special meaning for this VUMAT: SDV1Tensile damage along direction 1 (fiber direction)SDV2Compressive damage along direction 1SDV3Tensile damage along direction 2 (transverse direction)SDV4Compressive damage along direction 2 (transverse direction)SDV5Material point status; 1 if active, 0 if failedSDV6-11Components of viscous stresses if beta-damping is activeSDV12-17Components of elastic strain tensor


Unidirectional Fiber VUMATExample: Composite laminate plate ballistic impact


Unidirectional Fiber VUMATResults:


Unidirectional Fiber VUMATUsing cohesive elements for delamination prediction

Woven Fabric VUMAT


Woven Fabric VUMATA schematic of the assumed woven material is shown to the right.The fiber directions are assumed to be, and to remain, orthogonal (no wrinkling due to shear).The constitutive stress-strain relations are formulated in a local Cartesian coordinate system with base vectors aligned with the fiber directions.The fabric reinforced ply is modeled as a homogeneous orthotropic elastic material with the potential to sustain progressive stiffness degradation due to fiber/matrix cracking, and plastic deformation under shear loading.


Woven Fabric VUMATIt is assumed that the elastic stress-strain relations are given by orthotropic damaged elasticity.

Three global damage variables are used and are associated with fiber fracture along the 1- and 2-directions and matrix micro-cracking due to shear deformation.The model differentiates between tensile and compressive fiber failure modes by activating the corresponding damage variable depending on the stress state in the fiber directions


Woven Fabric VUMATFiber responseThe material response along the fiber directions is characterized with damaged elasticity. It is assumed that the fiber damage variables are a function of the corresponding effective stressThe criterion for initiation of fiber failure is assumed to take the form

Shear responseThe shear response is dominated by the non-linear behavior of the matrix, which includes both plasticity and stiffness degradation due to matrix microcrackingThe criterion for initiation of shear failure is assumed to take the form


Woven Fabric VUMATElement deletionThe VUMAT provides an option to delete elements when any one tensile/compressive damage variable along the fiber directions reaches a maximum specified value, or when the plastic strain due to shear deformation reaches a maximum specified value.CalibrationThe elastic constants and the fiber tension/compression strengths are easily measured from standard coupon tests in uniaxial tension/compression loading of 0/90 laminates.The calibration of damage evolution in the fiber failure modes is based on the fracture energy per unit area of the material, which can be measured experimentally.The shear response is usually calibrated with a cyclic tensile test on a 45 laminate, where the strains along the fiber directions can be neglected.


Woven Fabric VUMAT26 user material constants must be specified for this subroutineYoungs moduli in fiber 1- and 2-directions E1+/-, E2+/-Poissons ratio n12+, n12-Shear modulus G12Shear stress at the onset of shear damage STensile and compressive strength along fiber directions X1+/-, X2+/-Shear equation parameters a12, d12max


Woven Fabric VUMATEnergy per unit area for tensile and compressive fracture along fiber directions Gf1+/-, Gf2+/- Shear plasticity coefficientssy0, C, pControls for material point failure lDelFlag, dmax, eplmax, emax, emin


Woven Fabric VUMATData inputTo activate the model for fabric reinforced composites the material name must start with the string ABQ_PLY_FABRIC


Woven Fabric VUMATOutputIn addition to the standard output variables for stress-displacement elements, the following output variables have a special meaning for this VUMAT:SDV1Tensile damage along fiber direction 1SDV2Compressive damage along fiber direction 1SDV3Tensile damage along fiber direction 2SDV4Compressive damage along fiber direction 2SDV5Shear damageSDV6Tensile damage threshold along fiber direction 1SDV7Compressive damage threshold along fiber direction 1SDV8Tensile damage threshold along fiber direction 2SDV9Compressive damage threshold along fiber direction 2SDV10Shear damage threshold


Woven Fabric VUMATOutput (contd)SDV11Equivalent plastic strainSDV12Elastic strain component 11SDV13Elastic strain component 22SDV14Not usedSDV15Elastic strain component 12SDV16Material point status: 1 if active, 0 if failed


Woven Fabric VUMATExample: Composite woven fabric beam crush


Woven Fabric VUMATResults:

Modeling Techniques


Modeling TechniquesStable time incrementFor Abaqus/Explicit, the concept of the stable time increment is important to understand When modeling composites at the laminate level, very small element dimensions can be encounteredThis can lead to a very small stable time increment, requiring a large number of increments to complete an analysisFor a typical composite where Le=0.2 mm, r =1.5e-9, E=65 GPa, and n =0.3, Dt is on the order of 1e-10 seconds.To simulate 1 millisecond will require 10 million increments!Some ideas for dealing with this follow.


Modeling TechniquesStable time incrementUse double precision if the number of increments will exceed 300,000To attempt a more time economical solution, the following may be helpfulMass scaling can be used to speed up the simulation for the purposes of checking model setupDynamic response will be affectedGroup layers of common material orientation together and model as one layerUse continuum macroscopic (i.e., anisotropic global) properties to model the composite instead of using a mixed modeling technique


Modeling TechniquesInterior surfaces for erosionIf erosion will be considered in an impact analysis, care must be taken when defining contactInterior mesh surfaces must be included in the contact definitions

The inclusion of interior faces is not currently supported in Abaqus/CAE, and requires a manual edit to the input file. For example:*SURFACE, NAME=interior_elems, TYPE=ELEMENT all_elems, interiorThis creates a surface named interior_elems consisting of the interior faces of the element set all_elems, which can now be used in the contact domain

With the increasing use of composite materials in automobiles and aircraft, the ability of these structures to withstand impact is an important design consideration. Impact can be encountered both during automotive or aircraft crash, or as a result of debris from roads or runways. The top figure here depicts a head on collision test of two automobiles. The bottom figure shows the damage that can occur to a composite aircraft radome after a bird strike event.C_{ij} are damaged elastic constants.

Damaged elasticity refers to a gradual decrease in the material stiffness as damage accumulates. Once a material is fully damaged, the stiffness has decreased to zero. In this VUMAT, damage can occur in either tension or compression, and is calculated separately for the fiber and matrix components.The tension and compression components of damage are used to define a global damage parameter for the fiber and matrix as seen here. The global damage variables are then used to reduce the value of the elastic constants from their undamaged state (denoted by a superscript 0).The undamaged elastic constants are calculated from user defined material properties at the start of the simulation.19 material constants are required for use with the unidirectional fiber VUMAT. While this seems like a significant amount of information, we can see from looking at the inputs that these values are fairly straightforward. The elastic and shear moduli, as well as the values of Poissons ratio are required. Information is then needed to tell the VUMAT how strong the material is in shear, as well as in tension and compression in each primary direction. An optional damping parameter can be input as well to include material damping effects is they are significant to the problem under consideration.The input data for the unidirectional fiber VUMAT is shown here. Note that the number of material constants listed is 27, not 19. This is simply due to the fact that each data line must have eight values, however for some of these data lines (2 and 3) less than eight are used. Therefore 27 must be specified, with some of these values being 0 to fill out the inputs. The VUMAT also requires the user to tell it how many solution dependent variables are required. This VUMAT requires 17, and uses variable number 5 to control element deletion.By including SDV as an output variable in the Abaqus output requests, solution dependent outputs can be included as shown above. These variables allow you to determine the amount of tensile and compressive damage has occurred in the fiber and matrix at any point in the simulation.A view of the undamaged plate geometry. The plate has been fixed in all degrees of freedom around the edges. The ball velocity has been specified to impact the plate normal to the top surface.A view of the underside of the plate after penetration. The significant amount of damage done to the plate material is clearly evident. Many areas of the plate lower surface have been damaged even though they do not directly interact with the projectile. This occurs due to the extreme stress waves propagating through the plate material.While modeling at the ply level is an advantage when a detailed knowledge of failure behavior is desired, this is often not possible on real-life large structures. The model size would soon become unmanageable. Therefore it is typical to model a laminate using a coarse mesh and global material properties rather than individual lamina properties. In the example shown here, a 20 layer laminate plate was modeled using only 6 elements through the thickness. However, to include delamination in the model, cohesive elements were used in areas where significant delamination was expected. This is an economical way to minimize model size and yet include additional detailed physical failure mechanisms.The woven fabric VUMAT again uses damaged elasticity to account for degradation of material stiffness.As in most simulations of complex material behavior, it is important to calibrate the model using available data. This is often obtained from coupon tests of the constituent materials.24 user defined material constants are required for use with the woven fabric VUMAT. As we saw before, while this is a non-trivial amount of data, the inputs are straightforward. The elastic modulus in the two fiber directions for both tension and compression are required. In addition, Poissons ratios, the shear moduli and strength, as well as tensile and compressive failure stresses are required. Two additional inputs are required for use in the shear representation, however default values are provided for these inputs.24 user defined material constants are required for use with the woven fabric VUMAT. As we saw before, while this is a non-trivial amount of data, the inputs are straightforward. The elastic modulus in the two fiber directions for both tension and compression are required. In addition, Poissons ratios, the shear moduli and strength, as well as tensile and compressive failure stresses are required. Two additional inputs are required for use in the shear representation, however default values are provided for these inputs.This is an example of a sine-wave beam fabricated from a hybrid woven fabric/Kevlar composite. This type of structure is typical in areas where energy absorption for crashworthiness is desired. This type of beam would typically be found in the subfloor of a helicopter cockpit to absorb energy in the event of hard landing. Here a semi-circular impactor, defined as a rigid body, is dropped onto the top of the beam. The gold stripe is a ply drop-off location to initiate the desired crushing response.The results of the crushing analysis are shown here. The extreme amount of damage is clearly evident as the solution progresses. This is a desired result. The damage to the beam means that this energy will not be transferred to the pilots spine.

Composite Impact

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