# MATFAT

Bulk Data Entry Defines material properties for fatigue analysis.

## Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MATFAT MID UNIT LENUNIT
STATIC YS UTS
Optional continuation lines for SN Fatigue properties:
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
SN SRI1 B1 NC1 B2 FL SE
FINDLEY TFP MSS1 MSS2 MSS3 MSS4 A/R
Optional continuation lines for SN-based Spot Weld Fatigue properties:
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
SPWLD   MSS1 MSS2 MSS3 MSS4 R A/R
SR1_SP1 B1_SP1 NC1_SP1 B2_SP1 FL_SP1 SE_SP1
SR1_SP2 B1_SP2 NC1_SP2 B2_SP2 FL_SP2 SE_SP2
SR1_SP3 B1_SP3 NC1_SP3 B2_SP3 FL_SP3 SE_SP3
Optional continuation lines for SN-based Seam Weld Fatigue properties (Volvo Method):
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
SMWLD   MSS1 MSS2 MSS3 MSS4   A/R
SR1_SM1 B1_SM1 NC1_SM1 B2_SM1 FL_SM1 SE_SM1
SR1_SM2 B1_SM2 NC1_SM2 B2_SM2 FL_SM2 SE_SM2
Optional continuation lines for SN-based Seam Weld Fatigue properties (Joint Line Method). The following two blocks identify the SN curves for Seam Weld Joint Line method. The first block is for normal stress SN curve (mandatory) and the second block is for shear stress SN curve (optional):
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
SMWLD NORMAL MSSN1 MSSN2 MSSN3 MSSN4   A/R
SR1_SMN1 B1_SMN1 NC1_SMN1 B2_SMN1 FL_SMN1 SE_SMN1
SR1_SMN2 B1_SMN2 NC1_SMN2 B2_SMN2 FL_SMN2 SE_SMN2
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
SMWLD SHEAR MSSSH1 MSSSH2 MSSSH3 MSSSH4   A/R
SR1_SMSH B1_SMSH NC1_SMSH B2_SMSH FL_SMSH SE_SMSH
Optional continuation lines for multiple SN curve Fatigue properties:
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
SNTBL REFTYPE logSE Nc1 Nc FINDLEY STSTYPE
REFVAL1 A1 B1 A2 B2 A3 B3
A4 B4 A5 B5 ...
REFVAL2 A1 B1 A2 B2 A3 B3
A4 B4 A5 B5 ...
REFVAL3 A1 B1 A2 B2 A3 B3
A4 B4 A5 B5 ...
...
Optional continuation lines for EN Fatigue properties:
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
EN Sf b c Ef np Kp Nc
SEe SEp         A/R
tfp gfp bg cg CoefKp90 Coefnp90 MXLMSTRN
FSParm BMParm
Optional continuation lines for Factor of Safety (FOS) analysis:
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
FOS Tfl Hss STHETA SSHEAR
Optional continuation lines for Stress Gradient Effect:
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
STSGRD CRTDIS FKM_aG FKM_bG TFKM
Optional continuation lines for Fatigue Material Property Data:
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
SOLDER Wp Wcrp b1w Cp b1e

## Definitions

Field Contents SI Unit Example
MID Material identification number that matches the identification number on a MAT1 Bulk Data Entry.

No default (Integer > 0)

UNIT Defines the units of stress values specified on the YS, UTS, SRI1, FL, Sf, and Kp fields. Refer to Unit Systems for more information.
MPa (Default)
PA
PSI
KSI

MM
Millimeter
KM
Kilometer
M
Meter
CM
Centimeter
MI
Mile
FT
Foot
IN
Inch
Blank
Length unit is determined using the Stress unit, based on the following rules:
If Stress unit is MPa, then length unit is MM
If Stress unit is Pa, then length unit is M
If Stress unit is PSI or KSI, then length unit is IN

STATIC Indicates that static material properties are defined in the following fields.
YS Yield strength. 1

(Real > 0.0, or blank)

UTS Ultimate tensile strength. 1

(Real > 0.0, or blank)

SN Indicates that fatigue material properties for SN analysis are following.
SRI1 Fatigue strength coefficient. It is the stress range intercept of the SN curve at 1 cycle on a log-log scale.

No default (Real > 0.0)

B1 The first fatigue strength exponent. It can be input in two ways.
Real < 0.0
If a negative real number is input, then it is directly used as the slope of the first segment of the SN curve in log-log scale.
Real > 0.0
If a positive real number is input, then it is internally converted into -1/B1. This converted value is used as the slope of the first segment of the SN curve in log-log scale.

No default (Real ≠ 0.0)

NC1 In one-segment SN curve, this is the cycle limit of endurance (see NC1 in Figure 1).

In two-segment SN curve, this is the transition point (see NC1 in Figure 3).

No default (Real ≥ 1000.0)

B2 The second fatigue strength exponent. It can be input in two ways.
Real < 0.0
If a negative real number is input, then it is directly used as the slope of the second segment of the SN curve in log-log scale.
Real > 0.0
If a positive real number is input, then it is internally converted into -1/B2. This converted value is used as the slope of the second segment of the SN curve in log-log scale.

Default = 0.0 (Real)

FL Fatigue Limit. No damage occurs if the stress range is less than FL (see FL in Figure 1 and Figure 3). 6

(Real ≥ 0.0, or blank)

SE Standard Error of Log(N).

Default = 0.0 (Real ≥ 0.0)

FINDLEY Constant k in the Findley model

Default = 0.3 (Real > 0.0)

TFP Shear Fatigue Strength coefficient ( ${\tau }_{f}^{\text{'}}$ ) based on range. This value should be twice the value defined for TFP on the EN continuation line.

Default = Blank (Real > 0.0)

MSSi Mean Stress Sensitivity parameters for mean stress correction based on FKM Guidelines. These are used only if the UCORRECT field of the STRESS continuation line, on FATPARM, is set to FKM/FKM2 or the MCi fields of the MCORRECT continuation line, on FATPARM, is set to FKM. 11
MSS2
The MSS2 default is only applicable when MSS1, MSS2, MSS3, and MSS4 are all blank.
Default = 0.04 (Real > 0.0)
MSS1, MSS3, and MSS4
Default = blank (Real > 0.0)
Note: MSS1, MSS3, and MSS4 can be blank only if all of them are blank. If one of them is specified, then all four MSS1, MSS2, MSS3, and MSS4 should be input.

A/R
Defines the interpretation of the defined SN curve.
A
The SN curve is defined based on Amplitude.
R (Default)
The SN curve is defined based on Range.
Blank

SPWLD Indicates that the fatigue material properties for spot weld fatigue analysis are to follow. The following seam weld properties are only applicable to the Volvo method.
MSSi Mean Stress Sensitivity parameters for mean stress correction based on FKM Guidelines. These are used only if the UCORRECT field of the SPWLD continuation line on FATPARM is set to FKM or FKM2. 11
MSS2
The MSS2 default is only applicable when MSS1, MSS2, MSS3, and MSS4 are all blank.
Default = 0.04 (Real > 0.0)
MSS1, MSS3, and MSS4
Default = blank (Real > 0.0)
Note: MSS1, MSS3, and MSS4 can be blank only if all of them are blank. If one of them is specified, then all four of MSS1, MSS2, MSS3, and MSS4 should be input.

R Indicates the Stress Ratio, R, at which the Spot Weld SN curve is input 2 11

Default = 0.0. or -1.0

A/R
Defines the interpretation of the defined SN curve.
A
The SN curve is defined based on Amplitude.
R (Default)
The SN curve is defined based on Range.
Blank

SR1_SPi Fatigue strength coefficient. It is the stress range intercept of SN curve at 1 cycle in log-log scale.

Here i=1, 2, 3 represent sheet 1, sheet 2, and nugget, respectively in spot weld fatigue analysis.

For default 12 (Real > 0.0)

B1_SPi The first fatigue strength exponent. It is the slope of the first segment of SN curve in log-log scale.

Here i=1, 2, 3 represent sheet 1, sheet 2, and nugget, respectively in spot weld fatigue analysis.

For default 12 (Real < 0.0)

NC1_SPi In one-segment SN curve, this is the cycle limit of endurance (NC1 in Figure 1).

In two-segment SN curve, this is the transition point (NC1 in Figure 3).

Here i=1, 2, 3 represent sheet 1, sheet 2, and nugget, respectively in spot weld fatigue analysis.

For default 12 (Real ≥ 1000.0)

B2_SPi The second fatigue strength exponent. It is the slope of the second segment of SN curve in log-log scale.

Here i=1, 2, 3 represent sheet 1, sheet 2, and nugget, respectively in spot weld fatigue analysis.

Default = 0.0 (Real < 0.0 )

FL_SPi Fatigue Limit. No damage occurs if the stress range is less than FL (FL in Figure 1 and Figure 3). 6

Here i=1, 2, 3 represent sheet 1, sheet 2, and nugget, respectively in spot weld fatigue analysis.

(Real ≥ 0.0, or blank)

SE_SPi Standard Error of Log(N).

Here i=1, 2, 3 represent sheet 1, sheet 2, and nugget, respectively in spot weld fatigue analysis.

Default = 0.0 (Real ≥ 0.0)

SMWLD Indicates that the fatigue material properties for seam weld fatigue analysis are to follow. The following seam weld properties are only applicable to the Volvo method.
MSSi Mean Stress Sensitivity parameters for mean stress correction based on FKM Guidelines. These are used only if the UCORRECT field of the SPWLD continuation line on FATPARM is set to FKM or FKM2. 11
MSS2
The MSS2 default is only applicable when MSS1, MSS2, MSS3, and MSS4 are all blank.
Default = 0.04 (Real > 0.0)
MSS1, MSS3, and MSS4
Default = blank (Real > 0.0)
Note: MSS1, MSS3, and MSS4 can be blank only if all of them are blank. If one of them is specified, then all four of MSS1, MSS2, MSS3, and MSS4 should be input.

A/R
Defines the interpretation of the defined SN curve.
A
The SN curve is defined based on Amplitude.
R (Default)
The SN curve is defined based on Range.
Blank

SR1_SMi Fatigue strength coefficient. It is the stress range intercept of SN curve at 1 cycle in log-log scale.

Here i=1, 2 represent bending SN and membrane SN, respectively in seam weld fatigue analysis.

For default 13 (Real > 0.0)

B1_SMi The first fatigue strength exponent. It is the slope of the first segment of SN curve in log-log scale.

Here i=1, 2 represent bending SN and membrane SN, respectively in seam weld fatigue analysis.

For default 13 (Real < 0.0)

NC1_SMi In one-segment SN curve, this is the cycle limit of endurance (NC1 in Figure 1).

In two-segment SN curve, this is the transition point (NC1 in Figure 3).

Here i=1, 2 represent bending SN and membrane SN respectively in seam weld fatigue analysis.

For default 13 (Real ≥ 1000.0)

B2_SMi The second fatigue strength exponent. It is the slope of the second segment of SN curve in log-log scale.

Here i=1, 2 represent bending SN and membrane SN, respectively in seam weld fatigue analysis.

Default = 0.0 (Real ≤ 0.0)

FL_SMi Fatigue Limit. No damage occurs if the stress range is less than FL (FL in Figure 1 and Figure 3). 6

Here i=1, 2 represent bending SN and membrane SN respectively in seam weld fatigue analysis.

(Real > 0.0, or blank)

SE_SMi Standard Error of Log(N).

Here i=1, 2 represent bending SN and membrane SN respectively in seam weld fatigue analysis.

Default = 0.0 (Real ≥ 0.0)

SMWLD Indicates that the fatigue material properties for seam weld fatigue analysis are to follow. The following seam weld properties are only applicable to the Joint Line method. 15
NORMAL Flag indicates that the SN curve properties in this block are for Normal Stress. 15
MSSNi Mean Stress Sensitivity parameters for mean stress correction for Normal Stress SN curve based on FKM Guidelines. These are used only if the UCORRECT field of the SMWLD continuation line on FATPARM is set to FKM or FKM2. 11
MSS2
The MSS2 default is only applicable when MSS1, MSS2, MSS3, and MSS4 are all blank.
Default = 0.04 (Real > 0.0)
MSS1, MSS3, and MSS4
Default = blank (Real > 0.0)
Note: MSS1, MSS3, and MSS4 can be blank only if all of them are blank. If one of them is specified, then all four of MSS1, MSS2, MSS3, and MSS4 should be input.

A/R Defines the interpretation of the defined Normal Stress-based SN curve.
A
The Normal Stress-based SN curve is defined based on Amplitude.
R (Default)
The Normal Stress-based SN curve is defined based on Range.
Blank

SR1_SMNi Fatigue strength coefficient for Normal Stress-based SN curve. It is the stress range intercept of SN curve at 1 cycle in log-log scale.

Here i=1, 2 represent transverse SN and longitudinal SN, respectively for Normal Stress-based SN curve in seam weld fatigue analysis.

For default, 13 (Real > 0.0)

B1_SMNi The first fatigue strength exponent for Normal Stress-based SN curve. It is the slope of the first segment of SN curve in log-log scale.

Here i=1, 2 represent transverse SN and longitudinal SN, respectively for Normal Stress-based SN curve in seam weld fatigue analysis.

For default, 13 (Real < 0.0)

NC1_SMNi In one-segment SN curve, this is the cycle limit of endurance for Normal Stress-based SN curve (NC1 in Figure 1).

In two-segment SN curve, this is the transition point for Normal Stress-based SN curve (NC1 in Figure 3).

Here i=1, 2 represent transverse SN and longitudinal SN, respectively for Normal Stress-based SN curve in seam weld fatigue analysis.

For default, 13 (Real > 1000.0)

B2_SMNi The second fatigue strength exponent for Normal Stress-based SN curve. It is the slope of the second segment of SN curve in log-log scale.

Here i=1, 2 represent transverse SN and longitudinal SN, respectively for Normal Stress-based SN curve in seam weld fatigue analysis.

Default = 0.0 (Real < 0.0)

FL_SMNi Fatigue Limit for Normal Stress-based SN curve. No damage occurs if the stress range is less than FL (FL in Figure 1 and Figure 3). 6

Here i=1, 2 represent transverse SN and longitudinal SN, respectively for Normal Stress-based SN curve in seam weld fatigue analysis.

(Real > 0.0, or blank)

SE_SMNi Standard Error of Log(N) for Normal Stress-based SN curve.

Here i=1, 2 represent transverse SN and longitudinal SN, respectively for Normal Stress-based SN curve in seam weld fatigue analysis.

Default = 0.0 (Real > 0.0)

SMWLD Indicates that the fatigue material properties for seam weld fatigue analysis are to follow. The following seam weld properties are only applicable to the Joint Line method. 15
SHEAR Flag indicates that the SN curve properties in this block are for Shear Stress. The Shear Stress block is optional for Joint Line Seam Weld method. 15
MSSSHi Mean Stress Sensitivity parameters for mean stress correction for Shear Stress SN curve based on FKM Guidelines. These are used only if the UCORRECT field of the SMWLD continuation line on FATPARM is set to FKM or FKM2. 11
MSS2
The MSS2 default is only applicable when MSS1, MSS2, MSS3, and MSS4 are all blank.
Default = 0.04 (Real > 0.0)
MSS1, MSS3, and MSS4
Default = blank (Real > 0.0)
Note: MSS1, MSS3, and MSS4 can be blank only if all of them are blank. If one of them is specified, then all four of MSS1, MSS2, MSS3, and MSS4 should be input.

A/R Defines the interpretation of the defined Shear Stress-based SN curve.
A
The Shear Stress-based SN curve is defined based on Amplitude.
R (Default)
The Shear Stress-based SN curve is defined based on Range.
Blank

SR1_SMSH Fatigue strength coefficient for Shear Stress-based SN curve. It is the stress range intercept of SN curve at 1 cycle in log-log scale.

For default, 13 (Real > 0.0)

B1_SMSH The first fatigue strength exponent for Shear Stress-based SN curve. It is the slope of the first segment of SN curve in log-log scale.

For default, 13 (Real < 0.0)

NC1_SMSH In one-segment SN curve, this is the cycle limit of endurance for Shear Stress-based SN curve (NC1 in Figure 1).

In two-segment SN curve, this is the transition point for Shear Stress-based SN curve (NC1 in Figure 3).

For default, 13 (Real > 1000.0)

B2_SMSH The second fatigue strength exponent for Shear Stress-based SN curve. It is the slope of the second segment of SN curve in log-log scale.

Default = 0.0 (Real < 0.0)

FL_SMSH Fatigue Limit for Shear Stress-based SN curve. No damage occurs if the stress range is less than FL (FL in Figure 1 and Figure 3). 6

(Real > 0.0, or blank)

SE_SMSH Standard Error of Log(N) for Shear Stress-based SN curve.

Default = 0.0 (Real > 0.0)

SNTBL Flag to define multiple SN curves 17.
REFTYPE Reference type identifying the type of multiple SN curve definition.
MEAN
Ai, Bi data below represent multiple SN curves with respect to mean stress. The mean stress value for each SN curve is identified via REFVALi fields.
RRATIO
Ai, Bi data below represent multiple SN curves with respect to stress ratio. The stress ratio value for each SN curve is identified via REFVALi fields.
LIFE
Ai, Bi data below represent multiple Haigh diagrams with respect to life. The life value for each Haigh diagram curve is identified via REFVALi fields.

No default

logSE Standard Error of log(Stress)

Default = 0.0 (Real > 0.0)

Nc1 Fatigue transition point. After this point, fatigue strength is offset by the surface correction factor. Before this point, fatigue strength is proportionally reduced.

Default = NC (Real > 1000.0)

Nc Endurance limit. Number of cycles at which damage can be considered zero.

Default = 1.0E+8 (Real > 1.0E+5)

FINDLEY Constant k in the Findley model.

Default = 0.3 (Real > 0.0)

STSTYPE Stress type.
A
Amplitude.
R (Default)
Range.
MAX
Maximum stress.

REFVALi Reference values for which each curve is defined. Depending on REFTYPE, reference values can be either Mean stress, R-ratio or Life.

No default

Ai Depending on STSTYPE, Ai values can be one of stress amplitude, stress range, or max stress.

No default

Bi Depending on REFTYPE, Bi values can be life (REFTYPE=MEAN or RRATIO) or mean stress (REFTYPE=HAIGH).

No default

EN Indicates that fatigue material properties for EN analysis are following.
Sf Fatigue strength coefficient.

No default (Real > 0.0)

b Fatigue strength exponent.

No default (Real < 0.0)

c Fatigue ductility exponent.

No default (Real < 0.0)

Ef Fatigue ductility coefficient.

No default (Real > 0.0)

np Cyclic strain-hardening exponent.

No default (Real > 0.0)

Kp Cyclic strength coefficient.

No default (Real > 0.0)

Nc Reversal limit of endurance. One cycle contains two reversals. 6

Default = 2.0E8 (Real > 1.0E5)

SEe Standard Error of Log(N) from elastic strain.

Default = 0.0 (Real ≥ 0.0)

SEp Standard Error of Log(N) from plastic strain.

Default = 0.0 (Real ≥ 0.0)

A/R Defines the interpretation of the defined EN curve.
A (Default)
The EN curve is defined based on Amplitude.
R
The EN curve is defined based on Range.
Blank

tfp Shear Fatigue Strength coefficient ( ${\tau }_{f}^{\text{'}}$ ) based on amplitude. This value should be one half of the value defined for tfp on the SN continuation line.

Default = Blank (Real > 0.0)

gfp Shear Fatigue Ductility coefficient ( ${\gamma }_{f}^{\text{'}}$ )

Default = Blank (Real > 0.0)

bg Shear Fatigue Strength exponent ( ${b}_{\gamma }$ )

Default = $b$ (Real ≤ 0.0)

cg Shear Fatigue Ductility exponent ( ${c}_{\gamma }$ )

Default = $c$ (Real ≤ 0.0)

CoefKp90 Coefficient value (see Plasticity model for strain-based Fatigue Analysis in the User Guide).

Default = 1.2 (Real > 0.0)

Coefnp90 Coefficient value (see Plasticity model for strain-based Fatigue Analysis in the User Guide).

Default = 1.0 (Real > 0.0)

MXSTRN Maximum Strain value for Strain-Life Approach. The default value is 0.02 (corresponds to 2% strain).

In multiaxial fatigue analysis, this value is used as maximum allowable strain in the plasticity model regardless of whether the load is proportional or non-proportional. If accumulated strain is greater than this value, OptiStruct does not calculate actual damage but assigns a larger value of damage (10.0).

In uniaxial fatigue, 10% of this value (0.2% by default) is used as maximum possible strain amplitude. If strain amplitude is greater than 10% of this value, a warning message will be issued. Actual damage is still calculated.

Default = 0.02 (Real > 0.0) 14

FSParm Constant k for the Fatemi-Socie model.

Default = 0.3 (Real ≥ 0.0)

BMParm Constant S for the Brown-Miller model.

Default = 1.0 (Real ≥ 0.0)

FOS Indicates that material properties for factor of safety analysis are defined in the following fields.
Tfl Torsion fatigue limit. A Real or Integer value can be specified. If an integer is input, then it references the ID of a TABLES1 Bulk Data Entry that defines the intersection points. The X-values represent Hydrostatic Pressure, and Y-values represent Shear. 10

No default (Real > 0.0 or Integer)

Hss Hydrostatic stress sensitivity.

No default (Real > 0.0)

STHETA Safe zone angle. If the angle of a point in the domain is lower than the Safe zone angle, it is considered safe (FOS is 1.0e20). 10

Default = 0.0 (Real ≥ 0.0)

SSHEAR Shear Threshold for the Safe zone. If the microscopic shear stress is lower than this value, it is considered safe (FOS is 1.0e20). 10

Default = 0.0 (Real ≥ 0.0)

STSGRD Indicates that material properties for stress gradient effect are defined in the following fields.
CRTDIS Critical Distance for Critical Distance method in Stress Gradient Effect.
Real
Critical Distance.
Blank (Default)
Critical Distance is automatically estimated using Fatigue Limit and Young’s modulus. Refer to Stress Gradient Effect in the User Guide.

(Real)

FKM_aG ${a}_{G}$ value in FKM stress gradient effect.

Default = 0.5 (Real)

FKM_bG ${b}_{G}$ value in FKM stress gradient effect.

Default = 2700 (Real)

TFKM TABLES1 ID to define notch correction factor with respect to the related stress gradient in FKM stress gradient effect. If TFKM is specified, the relationship between related stress gradient and notch factor defined by TFKM takes precedence over FKM_aG and FKM_bG.

Default = Blank (Integer)

SOLDER Optional continuation line to define solder fatigue material property data.
Wp Plastic work density for Failure in DIFFCTE method. 16

Default = 0.0019 (Real > 0.0)

Wrcp Creep energy density for failure in SYEDW method. 24

Default = 0.0019 (Real > 0.0)

b1w Exponent of SYEDW method.

Default = -1.0 (Real)

Cp Inverse of creep ductility in SYEDEPS method. 24

Default = 0.0513 (Real > 0.0)

b1e Exponent of SYEDEPS method.

Default = -1.0 (Real)

## Figures

1. UTS or YS is used in mean stress correction (SN) and surface finish correction (SN and EN). If both UTS and YS are defined, UTS will be used. It is not allowed that both UTS and YS are blanks.
2. SN data defined in the MATFAT card is expected to be obtained from standard experiments that are fully reversed tests on mirror-polished specimens. Fully reversed tests imply that the stress ratio ( $R={S}_{\mathrm{min}}/{S}_{\mathrm{max}}$ ) is equal to -1.0. Therefore, any SN curve input on MATFAT entry should be obtained with a stress ratio (R) equal to -1.0.
Note: Only in the case of Spot Weld SN curve, the R field on the SPWLD continuation line can be used to indicate the stress ratio at which the input SN curve is obtained.
3. In SN approach, including Spot Weld and Seam Weld, OptiStruct calculates damage based on the Stress Range. If the SN curve is defined based on Stress Amplitude, OptiStruct converts the Amplitude-based SN curve to a Range-based SN curve. ECHO will print the converted SN curves. SN curves are defined in Stress range - Cycle form. Stress range is the algebraic difference between the maximum and minimum stress in a cycle. SN curve is expressed as:(1)
${S}_{r}=SRI1{\left({N}_{f}\right)}^{b}$
Where,
${S}_{r}$
Stress range
$SR1$
Fatigue strength coefficient
${N}_{f}$
Cycle number
$b$
Fatigue strength exponent
Note: For a special case, wherein the following two conditions are satisfied for SN Fatigue (Uniaxial and Multiaxial):
1. SRI1 is greater than 2*UTS, and
2. Stress amplitude after mean stress correction is greater than 90% of UTS.

Then, the equation used to calculate Fatigue Damage and Life is different from the SN curve mentioned above. Therefore, you may notice a sudden increase in the value of damage for an element when the above two conditions are satisfied for it. This is done to allow for the higher possibility of failure when the corrected mean stress is so close to UTS of the material, and additionally takes into account the situation where the value of SRI1 is extremely high (greater than 2*UTS).

4. In EN approach, OptiStruct calculates damage based on the Strain Amplitude. If the EN curve is defined based on Strain Amplitude, OptiStruct converts the Range-based EN curve to an Amplitude-based EN curve. ECHO will print the converted EN curves. EN curves are defined in Strain amplitude - Reversal form. Strain amplitude is half of the algebraic difference between the maximum and minimum strain in a cycle, and one strain cycle contains two reversals. EN curve is expressed as: (2)
${\epsilon }_{a}=\frac{{S}_{f}^{\text{'}}}{E}{\left(2{N}_{f}\right)}^{b}+{\epsilon }_{f}^{\text{'}}{\left(2{N}_{f}\right)}^{c}$
Where,
${\epsilon }_{a}$
Strain amplitude
${S}_{f}^{\text{'}}$
Fatigue strength coefficient
$E$
Young's modulus
${N}_{f}$
Cycle number
$b$
Fatigue strength exponent
${\epsilon }_{f}^{\text{'}}$
Fatigue ductility coefficient, and c is the fatigue ductility exponent
5. Empirical formula can be used to estimate SN/EN data from ultimate tensile strength (UTS) and Young's modulus ( $E$ ):
Table 1. Estimated SN Data from Empirical Formula*. (* Source: Yung-Li Lee, Jwo. Pan, Richard B. Hathaway and Mark E. Barekey. Fatigue testing and analysis: Theory and practice, Elsevier, 2005)
Material SRI1 b1 Nc1 b2
Steel 4.263*UTS -0.125 1E6 0.0
Aluminum alloys (UTS<336MPa) 2.759*UTS -0.062 5E8 0.0
Aluminum alloys (UTS≥336MPa) 0.131*UTS1.526 0.379-0.175*log(UTS) 5E8 0.0
Table 2. Estimated EN Data from UTS and E**. (** Source: Anton Baumel and T. Seeger, Materials Data for Cyclic Loading, Elsevier, 1990)
Unalloyed and Low-Alloy Steels Aluminum and Titanium Alloys
${\sigma }_{f}^{\text{'}}$ 1.5*UTS 1.67*UTS
$b$ -0.087 -0.095
${\epsilon }_{f}^{\text{'}}$ 0.59 $\Psi$ 0.35
c -0.58 -0.69
K' 1.65*UTS 1.61*UTS
n' 0.15 0.11
$\Psi =\left\{\begin{array}{l}1.0\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{\hspace{0.17em}}UTS/E\le 3×{10}^{-3}\\ 1.357-125*UTS/E\text{ }UTS/E>3×{10}^{-3}\end{array}\right\}$
6. For one-segment SN curve (b2=0.0), if FL is blank, the fatigue limit is the stress range at Nc1. If both Nc1 and FL are defined, the more conservative value (larger damage) will be used (Figure 1).

For two-segment SN curve, if FL is blank, the fatigue limit is 0.0.

When fatigue optimization is performed, fatigue limit FL of SN data and reversal limit Nc of EN data will be ignored in order to get continuous changes in fatigue results when stress/strain changes.

7. If tfp or gfp are not available, OptiStruct calculates this automatically. See Fatemi-Socie Model in the User Guide.
8. Although tfp is defined in EN, it can be used both in EN (FS model) and SN (Findley). tfp should be defined based on the amplitude.
9. If tfp is not defined for SN, OptiStruct calculates this automatically. See Findley Model in the User Guide.
10. The Tfl field can be used to define either a value (constant slope) or a table (multiple slopes) to specify the Failure zone. Additionally STHETA and SSHEAR fields can be used to determine safe-zones for FOS calculation.
11. See Mean Stress Correction in the Fatigue section of the User Guide for more information.
12. If SRI_SPi, B1_SPi, and NC1_SPi are not defined for Spot Weld Fatigue, then the following values are used as the default for the SN curve.
• Sheet 1: SRI_SP1=28218.0 MPa, B1_SP1=-0.34, NC1_SP1=2000000.0
• Sheet 2: SRI_SP2=28218.0 MPa, B1_SP2=-0.34, NC1_SP2=2000000.0

These default SN curves are based on a stress ratio (R) equal to 0.0

Only sheet damage (sheet 1 and sheet 2) at spot weld locations will be analyzed regardless of the value of SPTFAIL field on PFATSPW entry.

Mean stress correction for R=0.0 will be carried out using FKM guidelines regardless of the value of CORRECT field on SPWLD continuation line on FATPARM entry.

13. If SRI_SWi, B1_SWi, and NC1_SWi are not defined for Seam Weld Fatigue, then the following values are used as the default for the SN curve.
• Bending SN curve: SRI_SW1=3254.0 MPa, B1_SW1=-0.1429, NC1_SW1=2000000.0
• Membrane SN curve: SRI_SW2=6094.0 MPa, B1_SW2=-0.2270, NC1_SW2=2000000.0

These default SN curves are based on a stress ratio (R) equal to -1.0

14. In uniaxial fatigue, the calculated damage needs further checking, because the excessive strain implies that original analysis (static or transient) result could be beyond linear range.
15. For the Joint Line Seam Weld method, two SN curve blocks are available for input.

The first block (starting from field NORMAL on the SMWLD continuation line), defines the SN curves based on Normal Stress. There are two SN curve lines for this, the first is for Transverse Stress SN curve, and the second is for Longitudinal Stress SN curve. The Transverse Stress SN curve is mandatory, while the Longitudinal Stress SN curve is optional (if not input, then Fatigue Damage/Life is not calculated for Longitudinal Stress).

The second block (starting from field SHEAR on the SMWLD continuation line), defines the SN curve based on Shear Stress. This second block is optional (if not input, then Fatigue Damage/Life is not calculated for Shear Stress).

16. The default value for the SnAgCu solder is in MPa units.
17. SNTBL continuation line defines multiple SN curves/Haigh diagram for stress-life approach. Only one instance of SNTBL is allowed in a MATFAT entry.
18. SNTBL option is only supported in static analysis based fatigue and transient analysis based fatigue.
19. If a single Haigh diagram is defined, no damage will be calculated. Damage will be reported as 0.0. Only safety factor will be calculated if FOS output is requested.
20. If multiple SN curves/Haigh diagrams are defined, safety factor is calculated with an internally created target Haigh diagram. Refer to the User Guide for more details.
21. If multiple SN curves are defined, and mean stress correction is not INTPLTN, an SN curve with stress ratio =-1 or mean stress =0 has to be specified.
22. If multiple Haigh diagrams are defined, mean stress correction must be INTPLTN.
23. In multiaxial SN, any mean stress correction for tensile stress (FKM or GOODMAN) will trigger INTPLTN for damage due to tensile stress if multiple SN curves/Haigh diagrams are defined.
24. The default value if for SnAgCu solder represented by the hyperbolic creep material. The default value for Wcrp is in MPa units. In damage calculation, the default value for Wcrp is converted to that of user defined stress units in FATPARM.
25. This card is represented as a material in HyperMesh.