Response Surfaces for Stress/Strain curves
Stress/Strain Curves Extrapolated in Function of Material Properties with modeFRONTIER® modeFRONTIER® can be used to extrapolate stress/ strain curves in function of material properties, saving many material testing samples. This feature can be achieved through RSM
formed by the decreasing local cross-sectional
(Response Surface Methods), trained by testing
area) increases until the rupture or failure point.
Less ductile materials such as aluminium or brittle
During testing of a material sample, the stress–
materials like ceramics do not have a defined
strain curve is a graphical representation of
yield point, therefore the stress-strain curve would
the relationship between stress, derived from
consist mainly of elastic region, followed by the
measuring the load applied on the sample, and
failure of the material.
strain, derived from measuring the deformation
Testing of material samples are generally expensive
of the sample. The nature of the curve
and time-requiring, and to find a material with
varies from material to material.
required characteristics, it is usually necessary repeat testing on many samples until the expected
Steel generally exhibits a very linear
material is found.
stress–strain relationship up to a well
By modeFRONTIER® and its RSM (Response
defined yield point, and the slope is
Surface Methodology) tools, from an experimental
defined as the Young’s Modulus. As
database it is now possible to predict material
behaviour, such as true stress-strain curve and
increases until it reaches the ultimate
true strain failure, in function of material properties,
even if different from the database ones.
In addition, it is possible by a Virtual Optimisation, Until this point the cross-sectional area decreases,
to find optimal material properties that give a
while the true stresses (computed on the neck
required behaviour, saving many material testing.
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Stress Strain Curves Extrapolated in Function of Material Properties with modeFRONTIER®
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Programmes like modeFRONTIER® are most commonly used to optimise the design of systems, seeking to achieve user-defined goals (e.g. maximising efficiency or minimising pressure drops) by varying input parameters, and by defining a computational environment in which any CAE tool is coupled to allow a full automatic series of design runs, driven by an optimisation algorithm. Nevertheless, modeFRONTIER® includes many post-processing and analysis tools, such as RSM (Response Surface Methodologies), that allow to build a mathematical response of any system, starting from an available database. The RSM can then be used to extrapolate a response in function of a variation of the input parameters, or to produce a virtual optimisation (the output responses are not computed by a CAE tool or by an experimental test, but are obtained directly and instantly from the mathematical model), i.e. to find the combination of input parameters that give the optimal solutions. Example: RSM applied to Stress-Strain curves database To show how this procedure can be applied, an experimental database of stress-strain curves, relative to 14 different material samples, has been chosen. An Excel sheet contains data relative to 5 material physical or technological properties, that identify each different material (Young Modulus, Age, Temp, RTW, Pitch), and the corresponding True Strain and True Stress curve data, including the True Strain Failure data. Fig. 2
Database importing and RSM training The Excel sheet containing material database is imported in modeFRONTIER® through an easyto-use Data Wizard (Fig. 2), that step by step drives the user to select which columns contain input parameters and which ones contain output data (True stress and Strain failure). Once the database is imported (and a logic workflow is automatically built), the several database curves can be visualised (Fig. 3), and finally the RSM
can be automatically trained, using also in this case an easy-to-use RSM Wizard. At this point, a RSM function plot can be used to visualise a stress-strain curve in function of any combination of input material parameters (Fig. 4). RSM Function Plot By this feature, it is possible to compare extrapolated stress-strain curves with database
ones, and even to change input parameters in the dockable slide-bar menu, to have a
prediction of stress-strain curve for a material with modified property parameters (e.g., different Young Modulus, Age or RTW parameters). Virtual Optimisation to find optimal material parameters The RSM can be finally used to run a virtual optimisation, after having defined some goals to be achieved, such as maximise Young Modulus and True Strain Failure at same time. An optimisation algorithm (Multi-Objective-Genetic-Algorithm) obtains from the RSM the extrapolated outputs, and proposes several material properties combinations until the goals are achieved. In this case, the optimal material properties identify a stress-strain curve (Fig. 5, blue line) that seems to give better performances than original database ones.
modeFRONTIER® is a product of ESTECO Srl© 1999-2009 | www.esteco.com