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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 stresses within a selected individual ply in 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 stresses within a selected individual ply in 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 (x-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 applied stresses, due to an external load, must also be specified and are applied to the laminate as a whole. (There are no residual stresses.) The applied stresses must be expressed as components parallel (s_{x}), and normal (s_{y}) to the reference direction (x-direction), and as an in-plane shear stress (s_{xy}).

The program produces as output average values for the stresses within the selected ply. The components parallel (s_{1}) and normal (s_{2}) to the fibre axis and the shear stress (s_{12}) are written, as a function of angle between the loading direction and the reference direction, to 3 different files:

`<`- stress parallel to the fibre axis*filename*>.s1`<`- stress normal to the fibre axis*filename*>.s2`<`- shear stress in the plane of the ply*filename*>.t12

(<*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), 98-99. - Chapman and Hall, 1997,
*Mechanical Behaviour of Composite Materials*module in the MATTER educational software package. - MAP_COMP_LAMSTI

- 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 ply No. for which the output stresses are to be calculated.
- The applied normal stress in the x-direction (parallel to the reference direction) (MPa).
- The applied normal stress in the y-direction (perpendicular to the reference direction, in the plane of the ply) (MPa).
- The applied shear stress in the x-y plane (MPa).
- 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). |

s1 | - | Stress parallel to the fibre axis (MPa). |

s2 | - | Stress normal to the fibre axis (MPa). |

t12 | - | Shear stress in the plane of the ply (MPa). |

The following files are produced which contain the output:

`<`- angle phi and stress parallel to the fibre axis*filename*>.s1`<`- angle phi and stress normal to the fibre axis*filename*>.s2`<`- angle phi and shear stress in the plane of the ply*filename*>.t12

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.

Stresses within a loaded Laminate @ TW Clyne, Cambridge University, 1994 ref: An Introduction to Composite Materials, D.Hull & T.W.Clyne, CUP (1996), p.98-99 (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 stresses in selected ply, for general set of applied in-plane loads 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 0.31 [ 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 ply No. for stress output (>0 and < 8) 4 Enter applied normal stress in x-dir (MPa) 100 Enter applied normal stress in y-dir (MPa) 50 Enter applied normal stress in x-y plane (MPa) 5 Enter No. of phi values (max. 100) 5 Calculating...... Computation complete. Output is stored in 3 files. Enter prefix for these data files lamstr

Below are the output files:

lamstr.s1lamstr.s20.0000000000 102.07290359 0.0000000000 49.11417507 22.5000000000 98.11321342 22.5000000000 52.88869838 45.0000000000 81.15976447 45.0000000000 69.04935377 67.5000000000 61.14365720 67.5000000000 88.12944849 90.0000000000 49.79005578 90.0000000000 98.95212183lamstr.t120.0000000000 4.89337170 22.5000000000 -13.84054524 45.0000000000 -24.46685848 67.5000000000 -20.76081785 90.0000000000 -4.89337170

None.

composite, laminate, elastic constants, elastic, fibre, matrix, Young's, modulus, Poisson, shear, stress, 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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