Fatigue User’s Guide > Software Strain Gauges > Stress-Strain Analysis (MSSA)
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Stress-Strain Analysis (MSSA)
MSSA processes rosette data and creates outputs suitable for use by either the stress or strain-life fatigue analyzers. It also provides an indication of the state of multiaxiality present and suggests possible processing routes through the fatigue analyzers.
Additionally, MSSA can be used to convert elastic-plastic strain records, measured on one material, to that of another material. It can also convert elastic-plastic strain records to equivalent fully elastic ones and visa-versa.
MSSA processes data from either rectangular, delta or TEE rosettes. In addition, it can transform elastic- plastic strain records, measured on one material, to that of another material. It can also convert elastic-plastic strain records to equivalent fully elastic ones and vise-versa.
Strain Gauge Rosettes
Nomenclature for strain gauge rosette analysis:
Geometrically different, but functionality equivalent configurations of rectangular and delta rosettes are shown in Figure 11‑12 and Figure 11‑13.
Figure 11‑12 Rectangular Rosettes
Figure 11‑13 Delta Rosettes
By convention gauge numbering, 1,2,3 is counter-clockwise.
Rectangular Rosette
 
First strain gauge
Strain gauge at 45 to
Strain gauge at 90 to
Delta Rosette
 
First strain gauge
Strain gauge at 60 to
Strain gauge at 120 to
Transverse Sensitivity
 
Gauge (1) strain corrected for Poisson’s strain
Gauge (2) strain corrected for Poisson’s strain
Gauge (3) strain corrected for Poisson’s strain
Kt
Transverse sensitivity factor
Kt1
Transverse sensitivity factor for gauge (1)
Kt2
Transverse sensitivity factor for gauge (2)
Kt3
Transverse sensitivity factor for gauge (3)
Poisson’s ratio
p
Maximum principal strain
q
Minimum principal strain
max
Maximum shear strain
p
The angle from grid 1 to the max. principal
pq
The angle from grid 1 to either the max. or min. principal
p
Maximum principal stress
q
Minimum principal stress
max
Maximum shear stress
vm
Von Mises stress
Calculation of Principal Strains & Stresses
The following equations are used in the calculation of principal stress and strain from the component strains.
Rectangular Rosette
(11‑1)
(11‑2)
Delta Rosette
(11‑3)
(11‑4)
Tee Rosette
(11‑5) and
(11‑6)
(11‑7)
Maximum Shear Strain
(11‑8)
Maximum Shear Stress
(11‑9)
Von Mises Stress (under conditions of plane stress)
(11‑10)
Angle Between Grid 1 and the Maximum Principal Strain
Rectangular Rosette
(11‑11)
Delta Rosette
(11‑12)
Corrections for Transverse Sensitivity
Stacked Tee Rosette
(11‑13)
(11‑14)
Planar Tee Rosette
(11‑15)
(11‑16)
Stacked Rectangular Rosette
(11‑17)
(11‑18)
(11‑19)
(11‑20)
Planar Rectangular Rosette
When the transverse sensitivities of the orthogonal gages (1) and (3) are nominally the same.
(11‑21)
(11‑22)
(11‑23)
(11‑24)
Rectangular Rosette
In the case where all three transverse sensitivities are dissimilar.
(11‑25)
(11‑26)
(11‑27)
Stacked Delta Rosette
(11‑28)In this case
(11‑29)
(11‑30)
(11‑31)
Planar Delta Rosette
When the transverse sensitivity of two of the gauges, (1) and (3) are nominally the same
(11‑32)
(11‑33) 
(11‑34)
(11‑35) 
Delta Rosette
In the case where all three transverse sensitivities are dissimilar.
(11‑36) 
(11‑37) 
(11‑38) 
Elastic-plastic to Elastic Conversion
Using successive elastic-plastic strain ranges, , the corresponding stress range, is calculated from either,
(11‑39)
or,
(11‑40)
The equivalent elastic strain range, e, is calculated from
(11‑41)
Elastic to Elastic-plastic Conversion
Using successive elastic strain ranges, the corresponding equivalent elastic-plastic stress ranges are calculated from either,
(11‑42)
or,
(11‑43)
The equivalent elastic-plastic strain range, epsilon>, is calculated from
(11‑44)
Elastic-plastic to Elastic-plastic Conversion
This conversion uses the procedures described above to first convert the elastic-plastic strains to fully elastic ones using the first set of material properties, and then to convert these elastic strains to elastic-plastic strains using the second set of material properties.
MSSA Module Operation
The MSSA module can be run in one of the following three modes:
From the MSC.Fatigue menu driven system.
In stand alone mode by typing mssa at the system prompt.
By incorporating the MSSA commands in a batch or macro operation
The first two modes are interactive. Once running in interactive mode, the MSSA module will display the following main menu screen.
Figure 11‑14 The First MSSA Screen
Select option 1 of this menu to set up rosette calculations, and the other options are for strain conversions. See the technical overview for a definition of these terms.
Note that if rosette calculations had been previously carried out, then it is possible to go straight to the postprocessing menu (see Figure 11‑18) via the option 1 sub menu - Analyze or Display. The following text assumes that an analysis is being carried out.
Note also that Strain Gauge Rosette Analysis = Display uses graphics modules MMFD and MQLD to display plots
Each menu option will be explained, starting with option 1 - Strain Gauge Rosette Analysis.
1 - Strain Gauge Rosette Analysis
When option 1 is selected, the following screen is displayed. On it the user must define the type of rosette calculation to be undertaken.
Figure 11‑15 Specifying the Rosette Calculation
The fields are as follows:
:
Field
Description
Rosette Type
MSSA supports three types of rosette configuration: rectangular, delta and tee.
Tee rosettes consist of two mutually perpendicular grids.
Rectangular rosettes have three grids, with the second and third grids angularly displaced from the first grid by 45 and 90 degrees, respectively.
Delta rosettes have three grids, with the second and third grids 60 and 120 degrees away, respectively, from the first grid.
Rosette Construction
Strain gauge rosettes are manufactured in two forms: planar, and stacked.
Stacked rosettes have the three grids layered on top of each other.
Planar rosettes have all three grids lying in the same plane.
All the gauges in a stacked rosette have the same gauge factor and transverse sensitivity whilst the grids of a planar rosette will have slightly differing values of these properties. In the latter case, the transverse sensitivities of grids 1 and 3 are generally the same and grid 2 is different.
The ‘User’ field allows for the case when all three transverse sensitivities are different.
The rosette manufacturer’s data sheet should indicate the type of rosette that the analysis is being set up for.
The number of transverse sensitivities (see below) depends upon the choice made in this field.
Transverse Sens. Kt1 (%)
The transverse sensitivity coefficient, Kt, is defined as the ratio of the transverse and axial gauge factors. It is used to correct measured strains for the effects of transverse Poisson’s strains. It should not to be confused with the elastic stress concentration factor of the same name.
The number of values to be entered is:
One Stacked Rosette Configuration
Two Planar Rosette Configuration
Three User Defined Rosette Configuration
Enter the value of transverse sensitivity coefficient as a percentage. Please refer to the rosette manufacturer’s data sheet for the value(s) of this factor.
Gauge Poisson Ratio
Errors due to transverse sensitivity and the effect of Poisson’s strains in the calculation of stress from strain in anything other than a uniaxial field, may be corrected by using the Poisson’s ratio of the material on which the gauge or manufacturer’s factor was measured. For steel this value is usually, 0.285.
Please refer to the rosette manufacturer’s data sheet for the required value if different to the default.
Input From Files/Keyboard
MSSA can calculate principals, shears, and angles from strains measured by rosettes. These measured strains may be submitted as discrete values entered from the keyboard, or from data files containing any number of values.
Select whether strains are to be entered manually, or read from a disc file. Note that entering strains manually will allow a Mohr’s circle representation of the principal strains, or stresses to be displayed as shown in Figure 11‑16.
Note: The Keyboard option requires the user to specify the stress units, and then type the micro-strain values from the rosettes. MSSA will calculate the principles, angles, and shears in the normal way.
Output Type
This field only appears if Input From is set to Files. MSSA uses rosette strains to calculate principals and shears in terms of either stress or strain. The conversion from strain to stress values takes into account biaxiality caused by significant Poisson’s strains.
Stress Units
MSSA uses rosette strains to calculate principals and shears in terms of either stress or strain. The stresses can be calculated in a number of different unit systems. The conversion
MPa = 6.895 KSI is used
Note that the full units string, e.g. N/mm^2 must be used in conjunction with the batch keyword.
Young’s Modulus
The value of E is used in the principal stress option to convert from strain to stress.
Poisson Ratio
The value of mu is used in the principal stress option to convert from strain to stress. It is NOT the same value entered for the Gauge Poisson Ratio.
Graphical Results
When discrete Rosette Strains are entered from the keyboard, SSA offers the option of displaying the Rosette, the principals and the angle between the maximum principal and grid 1 in terms of a Mohr’s circle.
Graphical Operations
Figure 11‑16 Tabular and Graphical Results from Keyboard input (dependent upon Input Settings and Graphical Results Setting on Figure 11‑15)
 
Note:  
The statistics shown on the graphical display are rounded to the nearest integer. Values accurate to 3 significant figures are shown on the tabular display.
Operation of the graphics menu system is mostly standard MSC.Fatigue operations described elsewhere and in Module Operations (Ch. 17). However menu options of particular interest to MSSA are shown in the table below. The commands can be executed from a menu or at the command line. The menu options and command lines are briefly described below.
:
Option
Description 
General commands:
 
Strain\Stress circle
This toggles the display between the Mohr’s circle for stress and the Mohr’s circle for strain.
List Values
Lists all the values for stress and strain to maximum accuracy (3 significant figures).
New Options
Returns the user to the Input Options screen.
Exit
Will QUIT MSSA and return to the operating or menu system.
Graphics options in prompt mode:
 
HC
Hard copy (optionally HC=filename)
EX
Exit the program
PL
Replot. In batch, switches to interactive.
MCS
Show Mohr’s Circle for Stress.
MCE
Show Mohr’s Circle for Strain.
LV
List values numerically.
NV
Enter new values.
NOP
Modify options.
CU
Sets cursor mode.
Keys available in this mode and in menu mode:
 
P
Replots
H
Hardcopy of entire screen (including menu)
V
Display coordinate value
Q
Quits cursor mode
#
Go from menu mode to prompt mode
Input Files Screen
When all of the above parameters have been defined, the input file(s) screen must be completed.
Figure 11‑17 The Rosette File Option screen
This screen defines the input and output files to be used for rosette calculations. There are three different input files required for rectangular and delta rosettes or two for a tee rosette. Up to 7 output files will be created. Use the options on this screen to limit or configure the outputs.
 
Field
Description
Input File Names, E1, E2, and E3
MSSA calculates principals, angles and shears from strains measured by a rosette. Enter the name of the file that contains the rosette output, in MICROSTRAIN, from grids 1, 2, and 3 of a stain gauge rosette.
Note that for rectangular rosettes, grids 2 and 3 are angularly separated from grid 1 by 45 and 90 degrees respectively. For delta rosettes grids 2 and 3 are separated from grid 1 by 60 and 120 degrees respectively.
Alternatively, select the required file from the pick list of all .dac files present in the current directory by pressing the F3 key, or by clicking the LIST button with the mouse.
Files in other directories can be listed by specifying the appropriate path name. The required file can be selected by tagging with either the arrow keys or the mouse.
Generic Output Name
A number of output files, which contain the calculated stresses and strains will be created. These files will assume the generic name specified here and are distinguished from each other by different file extensions.
The following file extensions will be applied to the generic file name:
.max The maximum principal stress or strain.
.min The minimum principal stress or strain.
.abs The absolute maximum principal stress or strain.
.shr Either the absolute maximum or maximum shear stress or strain.
.ang The angle between grid 1and either the absolute maximum principal, or maximum principal, stress or strain.
.bax The biaxiality ratio of minimum to maximum principal.
.von The Von Mises stress.
Von Mises Output
MSSA can calculate the signed and unsigned Von Mises stresses directly from the principals.
The unsigned value is taken to be the positive root of the Von Mises expression. The signed value is taken to be a positive root with the sign of the absolute maximum principal given to it.
Either signed or unsigned Von Mises stress may be used directly in stress-based fatigue analyses.
If the None option is selected, then the Von Mises stress will not be calculated.
Shear Output
MSSA can calculate the maximum shear stress (or strain) from the two principal stresses (or strains) respectively.
The unsigned maximum shear strain is given by the difference between the two principal strains. The unsigned maximum shear stress is given by half the difference of the two principle stresses.
The signed maximum shears are calculated as above, BUT with the sign of the absolute maximum principal assigned.
Either the signed or unsigned maximum shear stresses and strains can be used directly in stress and strain-based fatigue calculations respectively.
If the None option is selected, then no shear values will be calculated.
Biaxiality Ratio
The biaxiality ratio is the ratio of the smaller in-plane principal stress to the larger (the absolute maximum principal). See Multiaxial Fatigue (Ch. 6) for more information.
It can take on values which range from -1 (pure shear), through zero (uniaxial), to +1 (equi-biaxial) loading.
As a rough guide, if the biaxiality ratio is greater than about +0.25 then fatigue calculations should employ a plane strain correction and use the absolute maximum principal strain as input.
In the band between +0.25 and -0.25, (basically uniaxial loading), fatigue calculations should use the absolute maximum principal as input.
For biaxiality ratios less than about -0.25, the absolute maximum principal can still be used or otherwise the maximum shear strain together with shear strain life fatigue properties.
If the No option is selected, then the biaxiality ratio will not be calculated.
Angle Option
MSSA can calculate the angle between the orientation of grid 1 of the rosette and either the maximum principal or the absolute maximum principal stress or strain
The variation of this angle with time through a loading history provides a valuable insight into the nature of the loading environment. It is sometimes useful to carry out a time at level analysis of the angle file in order to gauge angular stability. See also the graphical output options presented in the MSSA postprocessing menu.
If the angle is relatively stationary then the loading is said to be proportional, and simple uniaxial or shear models can be used in fatigue calculations.
If the angle fluctuates markedly, particularly at high strain amplitudes, then the loading is probably non-proportional and so fatigue analysis must use a critical-plane approach together with kinematic hardening models.
If the none option is selected, then the angle will not be calculated. See Multiaxial Fatigue (Ch. 6) for more information.
Biaxiality Gate
This value will be used to exclude any values of biaxiality for points whose absolute maximum principal strain is less than the gate.
When all of the above fields have been completed (or their defaults accepted), MSSA will process the input files according to the user’s specification. It will then display the Rosette Postprocessing menu which allows the results to be plotted.
Figure 11‑18 The Rosette Postprocessing Menu
At this stage the required output files have been created from the rosette strains and it is possible to display the results graphically.
Time series plots of all files can be plotted on a single display.
Crossplots of the biaxiality ratio or angle to grid 1 vs. absolute maximum principal can be also be displayed.
Finally, an amplitude distribution, time at level, can be created and plotted.
 
Note:  
MSSA uses the graphics module Multi File Display (MMFD) to plot the files. See Multi-File Display (MMFD), 224. From MMFD the user will always be returned to the Analysis Postprocessing menu.
2 - Elastic to Elastic-plastic Analysis
The purpose of this function is to convert a strain time history of elastic only data to an equivalent elastic-plastic strain time history file (assuming uniaxial loading).
Figure 11‑19 The Elastic to Elastic-Plastic Option Screen
The fields are as follows:
 
Field
Description
Input Filename
This is the name of the input file of elastic strain data. It is normally a single parameter file, e.g. test.dac.
Output Filename
Specify the name of the strain time history to create.
Kt
Specify the scaling factor to be used on the linearized data. This value is simply a strain multiplier or divisor. The stress concentration factor, Kt, may be used here to convert from nominal to local and vice-versa. When converting from elastic-plastic to elastic, this value is used as a divisor.
E-P Correction
This field allows you to choose the plastic stress correction type.
Shape Factor
Used in the Mertens-Dittmann and Seeger-Beste corrections. It is the ratio of the plastic limit load to the yield load.
Output Type
Select whether the output file will be in units of stress or strain.
When the above fields have been filled the Input Material Data Screen is displayed.
Figure 11‑20 The Input Material Data Screen
Figure 11‑21 The Materials Data Options
There are three ways of inputting materials data.
load from the materials database using the material name or picking from the F3/List pick list. The properties can be edited. PFMAT is the materials data source.
entered directly into the Young’s modulus, Cyclic exponent, and Cyclic coefficient fields.
generated from the material ultimate tensile strength (UTS) and Young’s modulus.
Specify the method to use. Depending upon the method chosen, one or more of the following fields will appear.
 
Field
Description
Material Name
All materials within PFMAT that have values for Young’s modulus and UTS are available. The List facility is probably the easiest way of scanning the database.
UTS (MPa)
The Ultimate Tensile Strength. The value of UTS is used to generate n’ and K’ (below). This field does not appear if Load or Enter are selected.
Young’s Modulus (MPa)
The value of E is used in the generation option to determine basic material type. If the data is loaded from the database this field will be modified each time the name is changed.
n’
n’ is the Cyclic Hardening Exponent. If the data is loaded from the database, or generated from the UTS and E, this field will be modified each time the name is changed or UTS/E are modified.
K’ (MPa)
K’ is the Cyclic Strength Coefficient (not to be confused with cyclic exponent above). If the data is loaded from the database, or generated from the UTS and E, this field will be modified each time the name is changed or UTS/E are modified.
When all of the above fields have been filled and accepted, the correction will be made and a results screen displayed. A sample results screen is shown below.
Figure 11‑22 An Elastic to Elastic-plastic Results Screen
3 - Elastic-plastic to Elastic Analysis
This option performs the opposite conversion to that described in option 2 - Elastic to Elastic-plastic Analysis, 884 above. However, all the screens and fields are the same as already described. Therefore, for usage instructions please refer to the option above.
4 - Elastic-plastic to Elastic-plastic Analysis
This option converts elastic-plastic strain records obtained with material A into an equivalent set of results that would have be achieved by material B. The basic steps are:
Name the input strain file (a single parameter data file), and the output file which will be created
Specify the input material data
Specify the output material data
The following fields need filling:
Input File Name name (see text for Figure 11‑19 above)
Output File Name (see text for Figure 11‑19 above)
Note that no Kf value is needed. The following need supplying for both input and output materials;
Input Method (see text for Figure 11‑20 above)
Material Name (see text for Figure 11‑20 above)
Young’s Modulus (see text for Figure 11‑20 above)
n’ (see text for Figure 11‑20 above)
K’ (see text for Figure 11‑20 above)
The post-analysis results screen is the same as for Figure 11‑18 above.
MSSA Batch Operation
MSSA can be run in batch mode.
An example batch or macro command line is shown below.
ssa /ov=y/opt=1/type=r/kt1=10/inp1=test101/inp2=test10
/inp3=test103/out=sumall
Which will carry out a rectangular (TYPE=R) strain gauge rosette analysis (OPT=1) with a stacked configuration (CON=S), transverse sensitivity (KT1) of 10%, and three INPut files. The family of output files will have the root name sumall, e.g. sumall.max, sumall.min, sumall.abs, sumall.shr.
Note that defaults were accepted for the other inputs.
A list of MSSA’s batch keywords:
 
/OPTion
The main option (1-4). /OPT=2
/INPut
The input filename. /INT=TEST1.DAC
/OUTput
The output filename. /OUT=RESULT.DAC
/KT
The scaling factor for conversion. /KT=1.5
/METH
Material entry method for input material, L, E, G. /METH=L
/MATname
Material name for input material. /MAT=RQC100
/UTS
UTS for input material. /UTS=900
/YM
YM for input material. /YM=2E5
/NP
n' for input material. /NP=0.15
/KP
K' for input material. /KP=1000
/METHOUT
Material entry method for output material. /METHOUT=G
/MATOUT
Material name for output material. /MATOUT=
/UTSOUT
UTS for output material. /UTS=900
/YMOUT
YM for output material. /YMOUT=2E5
/NPOUT
n' for output material. /NPOUT=0.3
/KPOUT
K' for output material. /KPOUT=1100
/MPOIS
Gauge Manufacturer's Poisson’s Ratio. /MPOIS=0.285
/TYPe
Rosette Type, R, D, T. /TYP=D
/CONfig
Rosette Configuration, S, P, U. /CONF=P
/KT1 ,/KT2 ,/KT3
Transverse sensitivity factors. /KT1=1.3
/INFRom
Input from File F or Keyboard K. /INFR=K
/OTYPe
Output Type - Stress S or straiN N. /OTYP=N
/CONversion
Stress Conversion - Linear or Non linear
/STSUNI
Stress Units (MPa,KSI,PSI). /STUNI=MPA
/GRAph
Whether to plot Mohr's Circle Y, N. /GRA=Y
/E1
First strain value. /E1=1E3
/E2
Second strain value
/E3
Third strain value
/INP1
File for gauge 1. /INP1=FILE1.DAC
/INP2
File for gauge 2. /INP2=FILE2.DAC
/INP3
File for gauge 3. /IINP3=FILE3.DAC
/OUT
Generic output name for rosette calculations. //OUT=FILES.
/VON
Von Mises output option signed S, unsigned U, none N. //VON=S
/SHEar
Shear output option signed S, unsigned U, none N. //SHE=S
/BIAX
Biaxiality ratio output yes Y, no N. /BIAX=Y
/ANGle
Angle output; maximum principle M, absolute maximum principle A, none N. /ANG=A
/POPTion
Post-processing option P, B, A, D, M, X (see main menu hot keys)