Method of measuring thermal properties of materials with direction dependant properties Technical field The present invention refers to a method for measuring thermal properties of a test substance by meanc vf a device incorporating a thin element or a layer of an electrically conductive material, e g metal, which is brought in heat conductive contact with said test substance, passing an electric current through said element or layer for supplying heat to the test substance and causing a temperature increase therein and recording the voltage variation over the element or the layer as a function of time and evaluate therefrom thermal properties, such as thermal conductivity and thermal diffusivity of the test substance, wherein the active part of said element or layer is in the form of a number of thin strips arranged in a circular pattern, Backgrozcnd of the invention Such a method is disclosed in US-A-5,044,767 according to which a plane heat source consisting of an electrically conducting pattern in the form of a double spiral is placed between two pieces of material to be tested. An electric current is passed through the element for supplying heat to the test material and causing the temperature therein to increase. The circular geometry of the element forms part of the theoretical model upon which the calculation of the thermal properties of the test material is based. In the disclosed method it is assumed that the test material is isotropic and does not show any direction dependant thermal properties.

However some materials and particularly certain composite materials have direction dependent thermal properties. This may be due to the specific design of layered structures or composites with for instance oriented fibres imbedded in a homogeneous matrix. It is also well known that materials like wood, certain minerals and biological materials often show strong direction dependent properties. Crystalline material further show direction dependant thermal properties. Normally it is a rather lengthy process to determine the thermal transport coefficients of materials with such properties.

Object antl most important features of the invention The object of the present invention is to provide a simplified method for determining the thermal properties for an anisotropic material having direction depending thermal properties, based on the method referred to above. This has according to the invention been achieved by measuring the thermal properties of a test substance of an anisotropic material for which the thennal properties are substantially the same in two orthogonal directions but different in the third orthogonal direction, placing the thin element or layer in parallel with the two directions of the test substance having substantially the same thermal properties, evaluating the experimental results by the following two thermal conductivity equation: for samples in which the thickness of the sample is >a and

for samples in which the thickness of the sample is <a ; where AT is the temperature increase as a function of time A, and 3 is the thermal conductivity in the first and third direction respectively of the test substance; at which A A3; a is the radius of the circular element; D (r,) and E are dimensionless time functions; , = (t/#) with the characteristic time Z/7c, and t is the experimental time measured from start of the transient and 7c, is the thermal diffusivity in one of the two directions having essentially the same thermal properties.

Description of the drawings The invention will hereinafter be further described with reference to an embodiment shown in the accompanying drawing which shows in a view from above an embodiment of a circular sensor element according to the invention.

Theoretical background In the above mentioned US-A-5, 044, 767, the disclosure of which herewith is included as a reference in the present application, a heat source/sensor with a conducting pattern in the form of a double spiral is described. In the theoretical model upon which the calculation of the thermal properties of the test material is based the assumption is made that the doub' ? spiral can be approximated by a number of concentric ring sources, at which one arrives at the following equation for the average temperature increase #T(#) assuming assuming that output output power Po is constant:: #T(#) = (A)α#)-1.D(#) where r= (t/d)'with the characteristic time B = c/K and t is the experimental time measured from the start of the transient, a is the radius of the outer concentric ring of the double spiral heat source and K is the thermal diffusivity of the sample material. Po is the total output of power in the double spiral heat source and A is the thermal conductivity of the sample material.

D (r) is a dimensionless time function given by the equation: where m is the number of equally spaced concentric rings of the double spiral heat source.

The actual evaluation of the experimental results is performed through an iteration process, where a computational plot of #Tversus D (r) is made by varying 0 and a time correction so that a straight line is obtained. This means that the thermal diffusivity can be determined as soon as the A-value is obtained, which gives a straight line plot of the temperature increase versus the dimensionless time function D (z).

From equation (A) it is also clear that the slope of the straight line can be used to directly determine the thermal conductivity of the sample material, since the output of power (P,)) as well as the radius (a) of the outer ring source are experimentally known parameters. Throughout the theory discussed above it has been assumed that the sample material is isotropic and does not show any direction dependant thermal properties.

The equation for the dimensionless time function D (T) stated above applies for infinite samples for which the temperature increase in the sensor is not influenced by the presence of any outside boundary of the sample.

For finite samples in the form of thermally insulated slabs of material, in which the thickness of the sample is <a and down to about 0.0 1-u, the time function E (T) is a bit different. This situation is disclosed in reference (II). The thermal insulation of the slab should be of such a nature that the heat loss from the slabs to the surroundings can be neglected in comparison with the total input of power to the two investigated slabs. The insulation can in most cases be achieved by placing a material with low thermal transport properties outside the slabs. It is also obvious that with such an arrangement only slabs with appreciably higher thermal conductivity than that of the insulating material can be studied with this experimental method.

The dimensionless time function E (r) will in this case be as follows: where h is the thickness of each of the two slabs of material on the sides of the sensor. The iteration process for determining the thermal diffusivity and the thermal conducti- vity from the transient recordings is done in exactly the same way as described above.

However there is an increased interest in materials for which the thermal properties display a direction dependence. According to the invention the thermal transport

properties can be determined from one single transient recording for such a material provided that the main directions in the material are orthogonal and can be referred to as the x-, y-and z-axes, and the thermal properties along the x-and y-axes are the same but different from those of the z-axis. The four transport parameters (thermal conduc- tivity and thermal diffusivity in the two orthogonal directions) can then conveniently be determined provide thc specific heat per unit volume of the anistropic material is known.

Thus let us assume that the principal directions in the material are orthogonal and that the thermal properties along two of these directions are the same. This is for instance the situation for a single uniaxial crystal. The above statements can be summarised in the following way: assume that the thermal properties are the same along the x-and y- axes but different from those along the z-axis.

In reference (III) the following equation is given for the temperature increase after a certain time in an anisotropic solid: where A, = pcp. K, A2 = pc K2 A3 = pCp K3 and where pcp is the specific heat per unit volume and K,, K2 and K3 is the thermal diffusivity of the sample material in the three orthogonal directions.

If we assume that the thermal properties along the x-and y-axes are the same, we can write down the solution for a ring source-if we only are interested in the temperature increase in the z-plane-accordingly:

With this equation as starting point we obtain the solution for an anisotropic material for which the thermal properties are the same in two directions but different from those of the third direction accordingly: where for infinite samples K, = K 3 and Al = #2 # #3 and

and ## = (tub,) with the characteristic time ## = α2/##.

For finite samples the dimensionless time function E (Ç,) is calculated according to:

Description of the invention According to the invention the thermal properties are determined for an anisoptropic material having direction dependant thermal properties in such a way that the principal directions of the material are orthogonal and that the thermal properties along two of these directions are the same, i e K, = K,-K3 and A, = A, = A3, wherein K is the thermal diffusivity and A is the thermal conductivity. This is for instance the situation for a single uniaxial crystal and composite materials, such as laminates, fiber reinforced materials, textile reinforced materials etc.

In the method there is used a plane heat source sensor 1 consisting of an electrically conducting pattern of thin metal strips la arranged in the form of a double spiral, which is sandwiched between two thin electrically insulating sheets (not shown). Preferably the electrically pattern is made of Ni or Pt, but can be made from any material for which the temperature coefficient of the electrical resisitivity is known. The electrical insulating sheets, both sides of the conducting pattern, are preferably made of Kapton, Mica or AIN, specially designed layers etc. The thickness of the conducting pattern is preferably about 10um and the insulating sheets preferably each has a thickness of between 25 and 100 um.

In the calculations above it has been assumed that the double spiral can be approxima- ted by a number of concentric and equally spaced ring sources. The radius of the outer concentric ring source is denoted a.

The heat source sensor 1 is placed between two pieces of material to be tested. Each of these pieces must have one flat surface so that the heat source sensor 1 can be fitted closely between the pieces. The sensor 1 must be placed in parallel with the two orthogonal directions of the material pieces in which the thermal properties are the same. That means that for a material piece having the same thermal properties in the x- and y-directions and differing from the thermal properties in the z-direction, the sensor 1 is placed in parallel with the xy-plane of the material piece.

The experiments and recordings are otherwise performed in the same manner as disclosed in US-A-5,044,767 and in references (I) and (II).

The evaluation of the experimental results is performed through the iteration process disclosed above, in which the expressions for A T (r,) and D (T,) or E (r,) respectively are used depending on whether the measurements are performed on samples of infinite or finite size respectively.

When performing the iteration to obtain a straight line from #T versus D(##) or E(##) respectively, we are actually determining the 0, and since ## = α2/## we can determine K, = K,, since we know the radius a of the sensor. In addition to this we get (#1 #3)1/2 from the slope of the straight line.

If we have informa.. lun on the specific heat per unit volume (pcp) from other measurements or from literature, we obtain directly: A, and x, as well as A3 and K3 which means that we have determined the thermal transport properties along the two orthogonal directions in the material. This is only possible if the plane of the sensor is placed in parallel with the plane defined by the x-and y-directions of the material and the thermal properties along these two directions are substantially the same.

For the finite sample the evaluation of the dimensionless time function E is a bit more complex since also the ratio of K/N3 appears. There are different ways of approaching this problem but one way is to use an iteration procedure with #1/#3 as an independent iteration variable.

References: [I] Silas E. Gustafsson:"Transient plane source techniques for thermal conductivity and thermal diffusivity measurements of solid materials", Rev. Sci. lustrum. 62 (3), 797 (1991) [II] Mattias Gustavsson, Ernest Karawacki and Silas E. Gustafsson:"Thermal conductivity, thermal diffusivity, and specific heat of thin samples from transient measurements with hot disk sensors", Rev. Sci. Instrum. 65 (12), 3856 (1994) [III] H. S. Carslaw and J. C. Jaeger,"Conduction of Heat in Solids" (Oxford. United Kingdom, 1959).