ANSYS ACP (Post) - Failure Criteria and Definitions

All available failure criteria are listed together with their failure mode abbreviations as used in failure mode plots.

Terms:

e = strain, s = stress
1 = material 1 direction, 2 = material 2 direction, 3 = out-of-plane normal direction, 12 = in-plane shear, 13 and 23 = out-of-plane shear terms
I = principal I direction, II = principal II direction, III = principal III direction
t = tension, c = compression

Criteria:

Maximum Strain: e1t, e1c, e2t, e2c, e12
Maximum Stress: s1t, s1c, s2t, s2c,s3t, s3c, s12, s23, s13
Tsai-Wu 2-D and 3-D: tw
Tsai-Hill 2-D and 3-D: th
Hashin: hf (fiber failure), hm (matrix failure), hd (delamination failure)
Puck (simplified, 2-D and 3-D Puck implementations are available): pf (fiber failure), pmA (matrix tension failure), pmB (matrix compression failure), pmC (matrix shear failure), pd (delamination)
LaRC 2-D and 3-D: lft3 (fiber tension failure), lfc4 (fiber compression failure under transverse compression), lfc6 (fiber compression failure under transverse tension), lmt1 (matrix tension failure), lmc2/5 (matrix compression failure)
Cuntze 2-D and 3-D: cft (fiber tension failure), cfc (fiber compression failure), cmA (matrix tension failure), cmB (matrix compression failure), cmC (matrix wedge shape failure)
Sandwich failure criteria:
- Wrinkling: wb (wrinkling bottom face), wt (wrinkling top face)
- Core Failure: cf
Isotropic failure criteria - Von Mises: vMe (strain) and vMs (stress)

Weighting factor: The inverse reserve factor of each failure mode is multiplied by the accordant weighting factor.

1: no safety
2: safety of two

Reserve Factor

The reserve factor indicates margin to failure. The applied load multiplied by the reserve factor gives the failure load:

Reserve factor values greater than one indicate positive margin to failure and values less than one indicate negative margin. The values of reserve factors are always greater than zero.

The critical values of reserve factors lie between zero and one, whereas the non-critical values range from one to infinity. Whether the results are shown in numeric form or as contour plots, the non-critical values tend to be emphasized in comparison to critical values. Therefore, the inverse reserve factor is often preferred in practical use:

The non-critical values of range from zero to one and the critical values from that on.

The margin of safety is an alternative for the reserve factor in indicating margin to failure. The margin of safety is obtained from the corresponding reserve factor with the relation

A positive margin of safety indicates the relative amount that the applied load can be increased before reaching failure load. Correspondingly, a negative margin of safety indicates how much the applied load should be decreased. Margins of safety are typically expressed as percentages.

TLDR:

Three failure mode measures are available:

IRF = Inverse Reserve Factor (IRF) defines the inverse margin to failure. Load divided with IRF is equal to the failure load. IRF >1 discloses failure.
MoS = Margin of Safety (MoS) defines the margin to failure. MoS is defined as (1/IRF - 1). MoS < 0 discloses failure.
RF = Reserve Factor (RF) defines the margin to failure. Load multiplied with RF is equal to the failure load. RF < 1 discloses failure.

Weighting Factor

Several failure criteria implemented in ACP are able to predict the failure mode, for example whether fiber or matrix failure occurs first. It is possible to assign weighting factors to individual failure mode criteria and thus create a certain bias towards or against a specific failure mode. As a result, failure criteria can be tuned to specific requirements. A design may require a higher safety against delamination than against fiber failure and the weighting factor of delamination is increased.

Using the maximum stress criterion as an example, the following shows the implementation of weighting factors in ACP:

TLDR: If you're worried about a specific failure mode more than another, add a weighting factor. This will be reflected in the likelihood of the failure criteria and failure mode that you have specified

Guide to Composite Failure Criteria

ACP-Post provides a number of failure criteria for the strength assessment of composites. Both established and basic as well as recent and advanced failure criteria are included in the program. This section provides some guidance on the selection of failure criteria.

It is advised that you use failure criteria that distinguish between different failure modes (for example, fiber failure or matrix failure).
The use of all-inclusive quadratic failure criteria is not advised (for example, Tsai-Wu, Tsai-Hill, or Hoffman). In most situations, these criteria are less accurate than others and provided minimal information on any failure.
It is more conservative to combine different failure criteria (Puck, Max Stress, and LaRC) than using any single criterion.
In general, failure criteria that consider all in-plane stresses (s1, s2, s12) and the out-of-plane interlaminar shear stresses (s13, s23) should be used, as these results are available in a shell model.
3-D stresses (s3) can often be ignored in thin laminates with moderate curvature. Otherwise, Puck 3-D can be used to investigate delamination.
3-D solid models can be used to get more accurate results, especially if out-of-plane stresses are being investigated.
Wrinkling and Core Failure should be evaluated for sandwich structures.
The use of Puck 2-D is recommended over the use of Puck Simplified.

Failure Criterion Function

The strength of materials and material systems under multiaxial loads can be predicted based on different failure criteria. Failure criteria relate the material strength allowables, defined for uniaxial tension-compression and shear, to the general stress-strain state due to multiaxial loads. Typically failure criteria are presented as mathematical expressions called failure criterion functions, which are functions of the stresses (or strains) and the material strength.

The values of failure criterion functions change with load similarly as the inverse reserve factor (values below one are non-critical and one indicates failure). However, the values are generally not equal except at the failure point. The reserve factordescribes the distance from the point of the applied load to the failure point. Typically a numeric line search method is used for determining the value ofbased on the selected failure criterion, stresses and strains due to the applied load, and material strength allowables.

Maximum Strain Criterion

In the maximum strain criterion, the ratios of the actual strains to the failure strains are compared in the ply principal coordinate system. The failure criterion function is written as

where:

Maximum Stress Criterion

In the maximum stress criterion, the ratios of the actual stresses to the failure stresses are compared in the ply principal coordinate system. Thus, the failure criterion function is

where:

Hashin Failure Criterion

In the Hashin criterion, criticality of tensile loads in the fiber direction is predicted with the expression:

Under compressive loads in the fiber direction, failure is predicted with an independent stress condition:

In the case of tensile transverse stress, the expression for predicting matrix failure is:

A more complex expression is used when the transverse stress is compressive:

Delamination (tension and compression) is predicted with this expression:

The most critical of the failure modes is selected:

Puck Failure Criteria

There are several different Puck Failure criteria, the following sections describe them.

Simple and Modified Puck Criterion

The two oldest Puck failure criterion formulations are simple Puck and modified Puck. Both criteria consider failure due to longitudinal loads and matrix failure mode due to transverse and shear loads separately ([27] and [28]).

For both the simple and modified Puck criteria, failure in fiber direction is calculated the same way as in the maximum stress criterion:

Matrix failure is calculated differently for each formulation as illustrated in Equation 5–61 for simple Puck. Equation 5–62 demonstrates how tensile or compressive failure stresses are used depending on the stress state.

where:

The modified Puck criterion differs from the simple criterion only in the formulation for matrix failure:

As in Hashin Failure Criterion, the failure occurs when either or reaches one, so the failure criterion function is:

Despite being called simple in the failure criteria configuration in the Failure Criteria Definition dialog the Puck modified version is actually implemented. The name is referring to the simplicity of that criterion in comparison to Puck's Action Plane Strength Criterion.

5.3.4.5.2. Puck's Action Plane Strength Criterion

The following sections describe the different failure modes for Puck’s action plane strength criterion.

5.3.4.5.2.1. Fiber Failure (FF)

As in the simple Puck criterion, one option for evaluating fiber failure is to use the maximum stress criterion for that case ([29], [30], and [31]):

and similarly a maximum strain criterion:

A more complicated version for FF criterion was presented by Puck for the World Wide Failure Exercise, but the maximum stress criterion is considered sufficient for the case of FF.

5.3.4.5.2.2. Interfiber Failure (IFF)

Interfiber failure is formulated differently depending on the model type.

Plane stress-state

Interfiber failure, or interfiber fracture ([29] and [30]) can be explained in the cutting plane for which the principal stress of a UD layer is zero in the case of plane stress.

Figure 5.6: Fracture Curve in σ₂, τ₂₁ Space for σ₁ = 0

The curve consists of two ellipses (modes and ) and one parabola (mode ). Generally Puck's action plane strength criterion is formed utilizing the following 7 parameters, , where stands for fracture resistances and for slope parameters of the fracture curves. The symbols and denote the reference to direction parallel to the fibers and transverse (perpendicular) to the fibers. The values for and define the intersections of the curve with -axis, as well as for the intersection with -axis. The slope parameters and are the inclinations in the latter intersections.

The failure conditions for IFF are:

The superscript denotes that the fracture resistance belongs to the action plane.

The assumption is valid here and leads to:

Equation 5–70 is also valid.

As the failure criterion functions and the functions for their corresponding stress exposure factors are the same, they can be written as follows (given Equation 5–69 and Equation 5–70):

3-D Stress State

While the latter formulations have been a reduced case working in ()-stress space, the 3-D stress state can be described with Equation 5–72:

where:

From the above equations, the failure criterion function is formulated in the fracture (action) plane using the corresponding stresses and strains. The formulations for the stresses , , and in an arbitrary plane with the inclination angle are:

To find the stress exposure factor the angle is iterated to find the global maximum, as the failure will occur for that angle. An analytical solution for the fracture angle is only available for plane stress-state by assuming:

which leads to formulations for the exposure factor:

Puck illustrated in [29] that the latter criterion can be used as a criterion to determine delamination, if an additional weakening factor for the interface is applied, finally resulting in:

The active failure mode depends on the fraction angle and the sign of . Delamination can occur if is positive and is 90 degree. The failure modes and happen with negative .

Puck Constants

Different default values for the coefficients are set for carbon and glass fiber plies to:

Carbon:

Glass:

Those values are compliant with recommendations given in [32].

Influence of fiber parallel stresses on inter-fiber failure

To take into account that some fibers might break already under uniaxial loads much lower than loads which cause ultimate failure (which can be seen as a kind of degradation), weakening factors can be introduced for the strength parameters. Puck formulated a power law relation in [29]:

where and and can be can be experimentally determined.

Different approaches exist to handle this problem numerically. The function given in Equation 5–77 can be replaced by an elliptic function:

where:

and

are degradation parameters.

In ACP, the stress exposure factor is calculated by intersecting the weakening factor ellipse with a straight line defined by the stress vector using the parameters:

Otherwise the fiber failure criterion determines the stress exposure factor .

Default values for the degradation parameters are and .

LaRC Failure Criterion

LaRC03 (2-D) and LaRC04 (3-D) are two sets of failure criteria for laminated fiber-reinforced composites. They are based on physical models for each failure mode and distinguish between fiber and matrix failure for different transverse fiber and matrix tension and compression modes. The LaRC criteria take into account that the apparent (in-situ) strength of an embedded ply, constrained by plies of different fiber orientations, is different compared to the same ply embedded in a UD laminate. Specifically, moderate transverse compression increases the apparent shear strength of a ply. Similarly in-plane shear significantly reduces the compressive strength of a ply. The evaluation of the in-situ strength also makes a distinction between thin and thick plies. The definition for a thick ply is a ply in which the slit crack is much smaller than the ply thickness. For epoxy E-glass and epoxy carbon laminates, the suggested threshold between thin and thick plies is 0.7 mm ([19] and [24]).

The implemented LaRC04 (3-D) failure criterion ACP assumes linear shear behavior and small angle deflection. The abbreviation LaRC stands for Langley Research Center.

LaRC03/LaRC04 Constants

The required unidirectional properties for the criteria are:

, , , , , , , , , , and .

where is the longitudinal shear strength and and are the fracture toughness for mode I and II.

The following LaRC Constants are required for postprocessing in ACP:

Fracture Toughness Ratio: (Dimensionless)
Fracture Toughness Mode I: (Force / Length)
Fracture Toughness Mode II: (Force / Length)
Fracture Angle under Compression: (Degrees)
Thin Ply Thickness Limit (Length)

The fracture angle can be determined in tests or taken to be which has proven to have good results for carbon/epoxy and glass/epoxy laminates [30]. The Thin Ply Thickness Limit is the only default value set for the LaRC parameters. The following reference values are drawn from [37]:

Parameter	Typical Values (Carbon/epoxy)
Elastic Modulus, (GPa)	128
Elastic Modulus, , (GPa)	7.63
Fracture Angle (deg)	53
Fracture Toughness Mode 1, (N/mm)	0.28
Fracture Toughness Mode 2, (N/mm)	0.79
Fracture Toughness Ratio, g	0.35
Thin Ply Thickness Limit (mm)	0.7

General Expressions

Several failure functions involve the friction coefficients, in-situ strengths, and fiber misalignment. These values are described in the following sections.

Friction Coefficients

Laminates tend not too fail in the plane of maximum shear stress. This is attributed to internal friction and considered in the LaRC failure criteria with two friction coefficients:

Transverse Friction Coefficient:

Longitudinal Friction Coefficient:

In-Situ Ply Strength

The in-situ transverse direct strength and longitudinal shear strength for a thin ply are:

where:

= thickness of an embedded ply

For a thick ply, the in-situ strengths are not a function of the ply thickness:

Fiber Misalignment Frame

Fiber compression, where the plies fail due to fiber kinking, is handled separately for transverse tension and transverse compression. In the model, imperfections in the fiber alignment are represented by regions of waviness, where transformed stresses can be calculated using a misalignment frame transforming the "original stresses". There are two different misalignment frames for LaRC03 (2-D) and LaRC04 (3-D).

LaRC03

For LaRC03, the stresses in the misaligned frame are computed as follows:

The misalignment angle for pure compression can be derived to 114 using and in the equations above as well as the stresses and the quadratic interaction criterion presented in Equation 5–93 for matrix compression.

The total misalignment angle is calculated from:

LaRC04

The 2-D misalignment model assumes that the kinking occurs in the plane of the lamina. LaRC04 incorporates a more complex 3-D model for the kink band formation. The kink plane is at an angle to the plane of the lamina. It is assumed to lie at an angle so that and is thus given by:

and the stresses rotated in this plane are:

Following the definition of a kink plane, the stresses are rotated into a misaligned frame. This frame defined by evaluating the initial and the misalignment angles for pure compression as well as the shear strain under the assumption of linear shear behavior and small angle approximation:

where:

= the misalignment angle for pure compression.

Following this, the stresses can be rotated into the misaligned coordinate system:

LaRC03 (2-D)

The following sections describe the failure modes for LaRC03 (2-D).

Fiber Failure

For fiber tension a simple maximum strain approach is applied:

Fiber compression failure for matrix compression is calculated as follows:

For fiber compression failure with matrix tension, the following quadratic equation has to be solved:

Matrix Failure

The formulation for matrix tensile failure is similar to that of fiber compressive failure under transverse compression. The difference is that the stress terms are not in the misaligned frame.

Matrix compression failure is divided into two separate cases depending on the longitudal loading. The failure function for the first case is:

where the effective shear stresses for matrix compression are based on the Mohr-Coulomb criterion which relates the effective shear stresses with the stresses of the fracture plane in Mohr's circle.

The transverse shear strength in terms of the transverse compressive strength and the fracture angle can be written as:

The failure function for the second case is:

where the effective shear stresses are rotated into the misaligned frame:

LaRC04 (3-D)

The following sections describe the failure modes for LaRC04 (3-D).

Fiber Failure

The LaRC04 fiber tensile failure criteria is simply a maximum allowable stress criterion with no interaction of other components:

Fiber compressive failure is divided into two components depending of the direction of the transverse stress. For transverse compression it is:

The failure function for fiber compression and matrix tension is based on the ANSYS Combined Stresses and Strains formulation for the LaRC criteria.

Matrix Failure

The failure function for matrix tension is based on the ANSYS Combined Stresses and Strains formulation for the LaRC criteria.

Matrix compressive failure is given by:

where:

Matrix compressive failure with transverse tension is given by:

Isotropic Material Failure

The failure criteria for isotropic materials is based on the von Mises stress (or equivalent stress in Mechanical):

or on the von Mises strain (or equivalent strain in Mechanical):

where and are the first and second principal strains. For isotropic material, the stress failure function is defined as:

and the strain failure function is defined as:

Failure Criteria vs. Ply Type Table

The table below illustrates which failure criteria evaluates the safety of the different ply types.

	Ply Type
Failure Criteria	Regular (UD)	Woven	Homogeneous Core	Honeycomb Core	Isotropic	Sandwich
Max Strain	√	√
Max Stress	√	√
Tsai-Wu	√	√
Tsai-Hill	√	√
Hofmann	√	√
Hashin	√
Puck	√	√ [1]
Cuntze	√
LaRC	√
Wrinkling						√ [2]
Core Failure			√	√
Von Mises					√

In combination with Puck for Woven specifications.
Sandwich is a laminate with at least one core layer.

Limitations and Recommendations

Interlaminar shear strains of linear triangular shell elements can not be evaluated. Interlaminar shear stresses of linear triangular shell elements can be evaluated by ANSYS but not by ACP. By default, the ANSYS .RST results file contains stress and strain data, however, they may be excluded. In the case of excluded stresses and strains, ACP can evaluate stresses and strains on the basis of the deformation and rotation fields in the results file. Nonlinear effects are not considered by ACP and can induce inaccurate stresses and strains. In general, it is recommended to include the stress and strain data in the .RST data. More information can be found in Solutions.

ACP provides a unique method to evaluate interlaminar normal stresses (INS) for shell elements. This calculation of the INS requires the evaluation of the shell curvature. It is therefore recommended to use quadratic shell elements when INS are of interest. The quadratic elements contain the curvature information per element and offer a better approximation than linear elements. The curvature for a linear shell element is determined from its neighboring elements. This evaluation does not consider INS induced by edge effects or out-of-plane loads (e.g. inserts, pressures, etc.).