The is the output from easigrow --list, slightly reformatted for markdown.
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Sequence filtering Performs sequence reordering, turning-point, dead-band, rise-fall filtering and rain-flow counting. The filtered sequences may be written to a file.
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Inbuilt data Comes with a selection of beta factors, material data and crack growth models.
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Calculated parameters Calculates additional parameters for characterising the state of the crack tip so that better crack growth equations can be developed based on the most applicable parameters for a material.
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Optimisation Optimises the crack growth model parameters to minimise the difference between predicted and measured crack growth. The measured data need not be for the entire history i.e., one or more fractographic measurements of the width of a block.
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Image generation Generates a pseudo fractographic image of the fracture surface to see how easy it is to identify the individual blocks.
The internal da/dN data are all in units for stress intensity of (MPa m^0.5) and growth in (m). Most beta equations use an applied far field stress which is in units of (MPa). However, the compact-tension beta factor compact_tada73 uses applied load not stress and is in units of load of (MN) and coupon dimensions are in (m). The width and depth will need to be set for the compact-tension beta function otherwise easiGrow will assume an infinite plate and the crack will not grow.
| Variable | Description |
|---|---|
| block | block number |
| line | line number |
| a/c | crack aspect ratio |
| a/d | cracked fraction of forward distance |
| c/b | cracked fraction of sideways distance |
| k | current cycle K |
| dk | current cycle dK |
| r | current cycle R |
| beta_a | beta factor at a |
| beta_c | beta factor at c |
| a | forward distance of crack from origin |
| c | sideways distance of crack from origin |
| da | crack growth increment at a |
| dc | crack growth increment at c |
| mono | largest monotonic plastic zone |
| cyclic | largest cyclic plastic zone |
| a/mono | ratio of crack length to monotonic plastic zone size |
| a/cyclic | ratio of crack length to cyclic plastic zone size |
| mono/da | ratio of current cyclic plastic zone to current da |
| cyclic/da | ratio of current cyclic plastic zone to current da |
| peak | scaled peak stress of current cycle |
| valley | scaled valley stress of current cycle |
| Beta | Variables | Description |
|---|---|---|
| qct-broek86 | quarter circular crack in an infinite plate in tension [broek86] | |
| seft-newman84 | a/d, a/c, c/b, phi | semi-elliptical surface crack in a finite plate in tension [Newman79] |
| seit-anderson05 | a/c, phi | semi-elliptical surface crack in an infinite plate in tension [Anderson05] |
| qcft-murakami87 | a/d | quarter circular corner crack in a finite plate in tension [Murakami87] |
| qeft-newman84 | a/d, a/c, c/b, phi | quarter elliptical corner crack in a finite plate in tension [Newman79] |
| eft-newman84 | a/d, a/c, c/b, phi | elliptical crack in a finite plate in tension [Newman79] |
| sset-tada73 | a/d | single sided edge crack in a plate in tension [Tada73] |
| dset-tada73 | a/d | double sided edge crack in a plate in tension [Tada73] |
| compact-tada73 | a/d, depth, width | compact specimen in tension (scale is in load units not stress units) [Tada73] |
| ct-fedderson66 | a/d | centre cracked plate in tension [Fedderson66] |
| ct-koiter65 | a/d | centre cracked plate in tension [Koiter65] |
| qcct-mcdonald07 | a/d | vertically constrained coupon with corner crack in tension [McDonald07] |
| ssht-bowie56 | a/r | single sided through crack in a circular hole in tension [Bowie56] |
| dsht-bowie56 | a/r | double sided crack through in a circular hole in tension [Bowie56] |
| dccht-newman81 | a/d, a/c, c/b, a/r, phi | double sided corner crack in a hole in tension [Newman81] |
| serbb-shin04 | a/d, a/c | semi-elliptical surface crack in a round bar in bending [shin04] |
| serbb-murakami87 | a/d, a/c | semi-elliptical surface crack in a round bar in bending [Murakami87] |
| serbt-murakami87 | a/d, a/c | semi-elliptical surface crack in a round bar in tension [Murakami87] |
| serbb-murakami86 | a/d, a/c | semi-elliptical surface crack in a round bar in bending [Murakami86] |
| serbt-murakami86 | a/d, a/c | semi-elliptical surface crack in a round bar in tension [Murakami86] |
| esb-murakami87 | a/d | edge crack in a strip in bending [Murakami87] |
| est-murakami87 | a/d | edge crack in a strip in tension [Murakami87] |
| file:FILE | a/d, a/c | read FILE for beta values |
Crack growth is calculated for each cycle. The cyles can be input directly or extracted from a sequence. The way the cycles are determined affects the growth. The methods for extracting cycles from a sequence are:
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rainflowCrack growth is calculated from rainflow cycles i.e. the stress intensity range comes from the range of the rainflow cycles. Note this has a slight re-ordering effect that may upset the order of any image plots created. -
tensionCrack growth calculated from tension part of cycle i.e. from a valley to the next peak. The striation pattern follows these tension cycles.
The da/dN model consists of EQUATION:material where the equation variable specifies the name of the da/dN equation and is one of [nasgro, paris, forman, walker, burchill, hartman, white, file] The material variable specifies the name of the parameters to use for that equation. If the values are given in --parameters they will be used instead of the standard library values.
| Name | Reference | Coefficients |
|---|---|---|
| paris:default | [none] | 1.00000e-10 3.00000e0 |
| walker:default | [none] | 1.00000e-10 5.00000e-1 3.00000e0 |
| forman:default | [none] | 1.00000e-10 3.00000e0 6.00000e1 |
| nasgro:default | [nasgro:aa7050t7451-LT, NASGR04.0] | 3.00000e-1 2.00000e0 3.51600e1 8.00000e-1 2.20000e0 1.00000e-1 1.00000e0 1.00000e0 6.35000e-10 2.50000e0 3.81000e-5 |
| nasgro:aa7050t7451-LT | [Forman05] | 3.00000e-1 2.00000e0 3.51600e1 8.00000e-1 2.20000e0 1.00000e-1 1.00000e0 1.00000e0 6.35000e-10 2.50000e0 3.81000e-5 |
| burchill:default | [none] | 1.00000e-10 3.00000e0 1.00000e-10 3.00000e0 |
| kujawski:default | [none] | 1.00000e-10 3.00000e0 5.00000e-1 |
| hartman:default | [none] | 1.00000e-10 1.00000e0 3.00000e1 3.00000e0 |
| paris:newman-aa7050t7451 | [none] | 1.59300e-11 3.66800e0 |
| forman:aa2024t3-sheet | [Schwarmann86] | 7.13000e-9 2.70000e0 7.13000e1 |
| forman:aa2024t351-plate | [Schwarmann86] | 5.00000e-9 2.88000e0 6.32000e1 |
| forman:aa2024t4-sheet | [Schwarmann86] | 8.57000e-9 2.60000e0 5.81000e1 |
| forman:aa2024t6-sheet | [Schwarmann86] | 2.00000e-8 2.62000e0 6.98000e1 |
| forman:aa2024t8-sheet | [Schwarmann86] | 1.33000e-8 2.65000e0 6.53000e1 |
| forman:aa2024t851-plate | [Schwarmann86] | 7.72000e-9 2.78000e0 6.14000e1 |
| forman:aa2219t851-plate | [Schwarmann86] | 4.84000e-8 2.16000e0 5.75000e1 |
| forman:aa2618t6-sheet | [Schwarmann86] | 8.56000e-9 2.58000e0 4.59000e1 |
| forman:aa6061t6-sheet | [Schwarmann86] | 2.27000e-7 6.01000e1 1.66000e0 |
| forman:aa6061t651-plate | [Schwarmann86] | 9.60000e-8 1.84000e0 4.12000e1 |
| forman:aa7010t73651-plate | [Schwarmann86] | 2.06000e-8 2.46000e0 4.60000e1 |
| forman:aa7050t7352-forging | [Schwarmann86] | 2.75000e-9 3.29000e0 6.40000e1 |
| forman:aa7050t73651-plate | [Schwarmann86] | 4.11000e-9 2.98000e0 5.50000e1 |
| forman:aa7075t6-sheet | [Schwarmann86] | 1.37000e-8 3.02000e0 6.39000e1 |
| forman:aa7075t7351 | [Schwarmann86] | 6.27000e-9 2.78000e0 5.58000e1 |
| forman:aa7175t3652-forging | [Schwarmann86] | 2.61000e-9 2.91000e0 3.80000e1 |
| forman:aa7178t651-plate | [Schwarmann86] | 3.74000e-8 2.06000e0 3.07000e1 |
| forman:aa7475t7351-plate | [Schwarmann86] | 3.24000e-8 2.32000e0 7.82000e1 |
| forman:aa7475t76-sheet | [Schwarmann86] | 6.54000e-8 2.18000e0 7.99000e1 |
| forman:aa7475t7651-plate | [Schwarmann86] | 9.30000e-9 2.73000e0 6.31000e1 |
| forman:a357t6-sandcasting | [Schwarmann86] | 2.19000e-9 2.94000e0 4.15000e1 |
| forman:a357t6-investmentcasting | [Schwarmann86] | 6.65000e-9 2.40000e0 3.82000e1 |
| hartman:jones13-aa7050t7451 | [jones13] | 7.00000e-10 1.00000e-1 4.70000e1 2.00000e0 |
| white:barter14-aa7050t7451 | [white15] | 2.54819e-1 1.10247e0 4.35832e0 2.30859e1 3.42017e-2 4.71784e-1 3.15400e1 |
| white:chan16-aa7050t7451 | [] | 2.91862e-1 1.26351e0 3.55283e0 2.22432e1 3.92409e-2 5.55131e-1 4.14592e1 |
| file:FILE | Read FILE of tabular dadn data. |
The crack growth file is in the following format:
<line> <block> <a>
...
or
<block> <a>
...
or
<a>
...
Blank lines in the file indicate non-contiguous measurements. If or are missing the program will assume the readings are one block apart with each block measured at line 0. Use the same format for the entire file. Where represents the corresponding line no. (starting at 0) of the sequence file, and is the no. of the block at that crack depth. Strictly speaking, the actual block numbers are not used by easigrow with only the difference between the block numbers in contiguous measurements used. Easigrow only matches the average crack growth rate using:
rate = (growth between measurements) / (no. of blocks between measurements).
Each line in the optimise file is a list of easigrow command lines (without the 'easigrow' command) with each line containing the easigrow options that will best reproduce the crack growth calculation for the associated crack growth curve that it is trying to match. Note: Only the material model specified by the main command line that invokes the optimisation will be used for all crack predictions, since those will be the parameters that are optimised. Any other material specifications will be ignored.
The format of the optimisation file is:
<easigrow option> ... --crack <FILE1>
<easigrow option> ... --crack <FILE2>
...
All lines beginning with a # are treated as a comment and ignored. The format of the beta file is
# Comment describing the contents of the file
a/d beta
...
All lines beginning with a # are treated as a comment and ignored. The format of the file is:
# Comment describing the contents of the file
r1 r2 ....
dadn1 deltaK1_r1 deltaK1_r2 ....
dadn2 deltaK2_r1 deltaK2_r2 ....
...
[Newman79] J. C. Newman , Jr. and I. S. Raju Analyses of surface cracks in finite plates under tension or bending loads NASA Technical Paper 1578 December 1979
[Newman81] J. C. Newman Jr. and I. S. Raju Stress intensity factor equations for cracks in three-dimensional finite bodies, NASA Technical Memorandum 83299, 1981 p 1--49.
[Newman81] J. C. Newman Jr. and I. S. Raju Stress-intensity factor equations for cracks in three-dimensional finite bodies subjected to tension and bending loads, NASA Technical Memorandum 85739, 1984.
[Anderson05] T. L. Anderson Fracture Mechanics - Fundamentals and Applications Taylor and Francis 3rd Edition 2005
[Tada73] H. Tada, P. C. Paris and G. R. Irwin The Stress Analysis of Cracks Handbook 1973
[Murakami87] Y. Murakami Stress Intensity Factors Handbook. Vol 2 Pergamon Press, Oxford, , 1987
[Murakami87a] Yukitaka Murakami and Hideto Tsuru Stress Intensity factor equations for a semi-elliptical surface crack in a shaft under bending 1986
[Schwarmann86] L. Schwarmann Material Data of High-Strength Aluminium Alloys for Durability Evaluation of Structures Aluminium-Verlag 1986 Note: The data from this report has been converted from mm/cycle to m/cyclic by factoring cf by 1e3.
[Fedderson66] Taken from Damage Tolerant Design handbook from AFGROW documentation.
[Kujawski01] Daniel Kujawski, A fatigue crack driving force parameter with load ratio effects International Journal of Fatigue, Vol 23, S239-S246, 2001
[Walker70] K. Walker The effect of stress ratio during crack propagation and fatigue for {2024-T3} and {7075-T6} aluminum Effects of Environment and Complex Load History for Fatigue Life, American Society for Testing and Materials,Special Technical Publication 462, 1970
[Jones12] Jones, R., Molent, L. & Walker, K.
Fatigue crack growth in a diverse
range of materials, International Journal of Fatigue Vol. 40,pages 43--50, 2012
[Hartman70] A. Hartman and J. Schijve The effects of environment and load frequency on the crack propagation law for macro fatigue crack growth in aluminum alloys, Engineering Fracture Mechanics, Vol. 1(4), 1970
[Shin04] C.S. Shin and C. Q. CAI Experimental and finite element analyses on stress intensity factors of an elliptical surface crack in a circular shaft under tension and bending, International Journal of Fracture 129: 239–264, 2004.
[Forman05] R. G. Forman, V. Shivakumar, J. W. Cardinal , L. C. Williams and P. C. McKeighan Fatigue Crack Growth Database for Damage Tolerance Analysis, DOT/FAA/AR-05/15, 2005.