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T.W. Clyne,

Composites and Coatings Group,

Department of Materials Science and Metallurgy,

University of Cambridge,

Cambridge, U.K.

__E-mail__

T.W. Clyne: twc10@cus.cam.ac.uk

Released: January 1998.

Added to MAP: October 1999.

This program calculates the elastic constants of a laminate (stack of plies), from the Young's modulus and Poisson ratio of fibre and matrix, the fibre volume fraction and the fibre orientation of each ply.

Language: | N/A |

Product form: | Executable files for use on almost any Apple Macintosh or PC. |

Complete Program.

Laminae, or plies, containing aligned fibres, generally have highly anisotropic elastic properties. The anisotropy can be reduced by stacking together plies with different fibre orientations and bonding them to form a laminate. The elastic properties of such a laminate can be predicted from those of the component plies, provided it is assumed to be thin and flat, has no through-thickness stresses, and edge effects can be neglected (Kirchoff assumptions) [1].

This basic laminate theory is used by the program to calculate the elastic constants of a laminate consisting of a number of plies which are stacked with the fibre axis of each at a specified angle to a reference direction. It is assumed that all the plies are the same (in terms of the elastic properties of the fibre and matrix materials, the fibre content, and the thickness of the ply), and that both matrix and fibre are transversely isotropic with the axis of symmetry along the fibre axis of the ply.

The axial and the transverse Young's moduli, the (axial-transverse) Poisson ratio and the (axial-transverse) shear modulus for both the fibre and matrix are required as input. (Note that, for isotropic materials, G=E/[2(1+nu)].) The axial Young's modulus and axial-transverse Poisson ratio of the ply are calculated using an equal strain (rule of mixtures) expression. The transverse Young's modulus and axial-transverse shear modulus of the ply are calculated using either equal stress or Halpin - Tsai expressions. The choice of model is made by giving an appropriate value for the input parameter Xi. In the Halpin-Tsai expressions Xi is typically about +1. If Xi is set to 0 then the expressions become identical to those obtained by the equal stress model.

The program produces as output the axial and transverse Young's moduli, the (axial-transverse) Poisson ratio and shear modulus, and the tensile-shear interaction compliance (S16bar). These are written, as a function of angle between loading direction and reference direction, to 5 different files:

`<`- axial Young's modulus*filename*>.eax`<`- transverse Young's modulus*filename*>.etr`<`- axial-transverse shear modulus*filename*>.gat`<`- axial-transverse Poisson ratio*filename*>.nat`<`- tensile-shear interaction compliance*filename*>.s16

(<*filename*> refers to a user-supplied name for the output files.)

__Downloading and running the program__

Compiled versions of the programs have been produced as stand-alone applications. They are run simply by double-clicking on the icon concerned. They should run on virtually any Apple Macintosh or PC. Data input is via the screen. Data output is to files which are named by the user. These are produced as files for the plotting application "Kaleidagraph", but they can be read as text files from many other plotting or spreadsheet applications. These output files are normally created within the currently-active folder. The program quits after each complete set of computations. For further use, it is necessary to double-click on the icon again.

The executable files for downloading have been compressed using STUFFIT EXPANDER on the Macintosh and WINZIP or PKUNZIP on the PC. These decoders can be downloaded from the following websites:

STUFFIT EXPANDER at `http://www.aladdinsys.com/expander/`

WINZIP at `http://www.winzip.com/`

- D. Hull and T.W. Clyne, 1996,
*An Introduction to Composite Materials*, (Cambridge: Cambridge University Press), 93-95. - Chapman and Hall, 1997,
*Mechanical Behaviour of Composite Materials*module in the MATTER educational software package.

- Axial Young's modulus of the matrix (GPa).
- Transverse Young's modulus of the matrix (GPa).
- Axial Young's modulus of the fibre (GPa).
- Transverse Young's modulus of the fibre (GPa).
- Axial-transverse Poisson ratio of the matrix.
- Axial-transverse Poisson ratio of the fibre.
- Axial-transverse shear modulus of the matrix (GPa).
- Axial-transverse shear modulus of the fibre (GPa).
- Xi value - typically about +1 for Halpin-Tsai terms. Set to 0 for the Equal Stress Model.
- Volume fraction of the fibre (between 0 and 1).
- Number of plies (between 1 and 20).
- The angle (degrees) between the reference direction and the fibre axis for each ply in the laminate.
- The number of different orientations between the loading direction and the reference direction for which calculations are to be performed over the angular range 0 to 90 degrees.

phi | - | The angle between the loading direction and the reference direction (degrees). |

Eax | - | Young's modulus of the laminate in the axial direction (GPa). |

Etr | - | Young's modulus of the laminate in the transverse direction (GPa). |

Gaxtr | - | The axial-transverse shear modulus of the laminate (GPa). |

nuaxtr | - | The axial-transverse Poisson ratio of the laminate. |

S16bar | - | The tensile-shear interaction compliance of the laminate (GPa^{-1}). |

The following files are produced which contain the output:

`<`- angle phi and axial Young's modulus*filename*>.eax`<`- angle phi and transverse Young's modulus*filename*>.etr`<`- angle phi and axial-transverse shear modulus*filename*>.gat`<`- angle phi and axial-transverse Poisson ratio*filename*>.nat`<`- angle phi and tensile-shear interaction compliance*filename*>.s16

None.

No information supplied.

Further information about this program can be obtained from the Composites and Coating Group website at http://www.msm.cam.ac.uk /mmc/mmc.html and is one of a series of programs produced by Bill Clyne and co-workers in the Materials Science Department at Cambridge.

It should be noted:

Nothing is expected of anyone downloading a program and there is no obligation to use results obtained from it in any particular manner. Equally, there is no liability on the part of the supplier and no guarantee that the programs do not incorporate errors or invalid data. In general, however, the offer is aimed at researchers and is designed to stimulate collaborative work. Anyone downloading a program is therefore invited to give their address to the supplier and is also welcome to enter into contact if they wish to explore any details. In the event that results obtained using any of the programs are published in any form, it would be appreciated if their source could be acknowledged.

Complete program.

Elastic constants of a Laminate @ TW Clyne, Cambridge University, 1994 ref: An Introduction to Composite Materials, D.Hull & T.W.Clyne, CUP (1996), p.93-95 (Unlimited distribution version - please acknowledge when publishing) Application of basic Laminate Theory (Kirchoff assumptions). Stack of plies, fibre axis of each at specified angle to reference direction. All plies same (fibre & matrix properties, fibre content & ply thickness). For fibre & matrix, both axial & transverse Young's moduli are input, but only single values of (axial-transverse) Poisson ratio & shear modulus input. Ply axial Young's modulus and axial-transverse Poisson ratio are calculated using an equal strain (rule of mixtures) expression. Ply transverse Young's modulus and axial-transverse shear modulus are calculated using either equal stress or Halpin - Tsai expressions. Treatment thus incorporates some approximations, but is fairly accurate. Output of axial & transverse Young's moduli, (axial-transverse) Poisson ratio & shear modulus, & tensile-shear interaction compliance (S16bar), all as function of angle between loading direction & reference direction. Enter matrix axial Young's modulus (GPa) 167 Enter matrix transverse Young's modulus (GPa) 167 Enter fibre axial Young's modulus (GPa) 34.1 Enter fibre transverse Young's modulus (GPa) 34.1 Enter matrix (axial-transverse) Poisson ratio 0.31 Enter fibre (axial-transverse) Poisson ratio 0.3 [ Note that, for isotropic materials, G=E/(2(1+nu)) ] Enter matrix (axial-transverse) shear modulus (GPa) 63.7 Enter fibre (axial-transverse) shear modulus (GPa) 13.0 Enter xi value (typically + 1) for Halpin-Tsai terms (0 for Equal Stress model) 1 Enter fibre volume fraction (0 to 1) 0.12 Enter number of plies (1 to 20) 7 Enter angle (degrees) between ref. dirn. & fibre axis for ply No. 1 0 Enter angle (degrees) between ref. dirn. & fibre axis for ply No. 2 45 Enter angle (degrees) between ref. dirn. & fibre axis for ply No. 3 -45 Enter angle (degrees) between ref. dirn. & fibre axis for ply No. 4 0 Enter angle (degrees) between ref. dirn. & fibre axis for ply No. 5 45 Enter angle (degrees) between ref. dirn. & fibre axis for ply No. 6 -45 Enter angle (degrees) between ref. dirn. & fibre axis for ply No. 7 0 Enter No. of phi values (max. 100) 5 Calculating...... Computation complete. Output is stored in 5 files. Enter prefix for these data files lamsti

Below are the output files:

lamsti.eaxlamsti.etrphi Eax(GPa) phi Etr(GPa) 0.0000000000 146.53018945 0.0000000000 142.87140274 22.5000000000 146.25493491 22.5000000000 143.65841725 45.0000000000 145.21341959 45.0000000000 145.21341959 67.5000000000 143.65841725 67.5000000000 146.25493491 90.0000000000 142.87140274 90.0000000000 146.53018945lamsti.gatlamsti.natphi Gaxtr(GPa) phi nuaxtr 0.0000000000 55.54994919 0.0000000000 0.31357363 22.5000000000 55.39301267 22.5000000000 0.31111977 45.0000000000 55.23696039 45.0000000000 0.30705268 67.5000000000 55.39301267 67.5000000000 0.30559635 90.0000000000 55.54994919 90.0000000000 0.30574385lamsti.natphi S16bar(GPa-1) 0.0000000000 0.00000000 22.5000000000 0.00003629 45.0000000000 0.00008738 67.5000000000 0.00008729 90.0000000000 0.00000000

None.

composite, laminate, elastic constants, elastic, fibre, matrix, Young's, modulus, Poisson, shear, stress, strain, compliance, equal stress model, Halpin-Tsai, ply

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MAP originated from a joint project of the National Physical Laboratory and the University of Cambridge.
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