Properties
Material Specific Properties of Duocel® Foams
Unlike surface area and fluid flow pressure drop which are strictly properties of the foam structure, most foam properties are at least partially affected by the foam base material.
Foam density - The actual density of a piece of foam is simply the bulk density of the base material of the struts or ligaments multiplied by the relative density.
Actual foam density = solid strut density × foam relative density
Typical foam relative densities:
Metal foams = ~2%min to ~ 15% max ( ~4% to ~ 10% typical useful range)
Carbon foams = 3% to 4% typical
Ceramic foams = ~3% min to ~20% max (~ 6% to ~ 12% typical useful range)
For actual foam density data, please refer to the metal foam, carbon foam or ceramic foam sections.
While foam products are always accompanied with material data including the relative density, the customer can easily reproduce or confirm this data. Simply weigh and measure the part, then divide the measured weight by the calculated weight if one were to assume the part were 100% solid material.
Thermal conductivity - The total thermal conductivity Ctotal of an open celled foam actually consists of four components as noted below:
Ctotal = Csolid ligaments + Cgas + Cgas convection + Cradiant
Where
Csolid ligaments = the conductivity of the three-dimensional array of solid ligaments or struts that form the foam structure. This term is also often referred to as the “bulk conductivity” of the foam. In most applications, particularly for metal foams used as heat exchangers, this is the quantitatively largest and most thermally dominant of the four components and has the following simplified equation form:
Csolid ligaments = Csolid × relative density × .33
Where
Csolid ligaments = direct thermal conductivity or bulk conductivity of the ligament array
Csolid = conductivity of the solid material of the struts
Relative density = % relative density in decimal form, i.e. 10% = .1
.33 = coefficient representing the foam structure geometric or “tortuosity” factor.
It should be noted that the .33 coefficient is derived both from conductivity tests and conceptual analysis wherein the foam can be analogized to a three-dimensional orthogonal pin fin array. In this case is it obvious that one third of the pins or pin mass are oriented in each of the orthogonal x, y, and z directions.
It should also be noted that this equation is somewhat simplified, but is reasonably accurate, slightly conservative, and is more easily understood from a conceptual standpoint than some of the empirical equations that have been developed from various tests.
Cgas = the bulk conductivity of any gas contained within the open-celled foam. It is usually a small contributor for metal foams, but can be a significant contributor with carbon or ceramic foams that have inherently low ligament material conductivity. Refer to the chart of RVC carbon foam conductivity to see a typical example of this effect.
Cgas convection = the conductivity of any gas contained within the cells and which can circulate within the foam or within the individual foam cells. Again, this is also a small contributor for metal foams, but can become significant when dealing with carbon or ceramic foams used as insulation. In such cases, small pore size 80 – 100 PPI foams are used to suppress this effect simply by increasing the foam specific surface area and gas flow pressure drop to the point where convection flow is effectively prevented.
Cradiant is the Infra-red electromagnetic radiation that transmits through the open apertures of the foam. This conductivity element is only of importance if the temperatures are very high and typically does not come into play unless the foam is being used as high temperature insulation. In such cases, the smallest pore size foam is typically used to suppress the view factor and increase the optical opacity of the foam.
Electrical Conductivity - Duocel foams are often used as porous electrodes, thus predicting the electrical conductivity is a valuable design tool. It should be no surprise that the low amperage, direct current bulk electrical conductivity of Duocel foam has the same form of equation as that for the bulk thermal conductivity. In its electrical form, it is:
Csolid ligaments = Csolid × relative density × .33
Where
Csolid ligaments = low amperage direct current electrical conductivity of the 3-D ligament array
Csolid = conductivity of the solid material of the struts
Relative density = % relative density in decimal form, i.e. 10% = .1
.33 = coefficient representing the foam structure geometric or “tortuosity” factor.
It should be noted that the .33 coefficient is derived both from conductivity tests and conceptual analysis wherein the foam can be analogized to a three-dimensional orthogonal pin fin array. In this case is it obvious that one third of the pins or pin mass are oriented in each of the orthogonal x, y, and z directions.
It should noted, as with the thermal form of the equation, that this is a somewhat simplified form that does not address electrical transients, alternating current, or large amperages where induced electromagnetic effects may significantly alter the predicted conductivity.
Foam modulus - When a load is applied to a foam structure, the foam will initially yield elastically. The slope of this initial stress / strain curve is the defined by the stiffness of the foam. The stiffness or Young’s Modulus of a foam structure is a function of the solid material modulus and the square of the foam structure relative density in the rather simple and elegant equation:
Modulusfoam = Modulussolid × relative density2
Where
Modulusfoam = Young’s Modulus of the isotropic foam structure
Modulussolid = standard Young’s Modulus of the solid strut material
Relative density = % foam relative density in decimal form, i.e. 1% = .1
Unlike foam density, and thermal or electrical conductivity, which are direct functions of the foam relative density, the modulus of the foam structure is a squared function of the relative density. This dominance of relative density in controlling foam modulus over a very wide range provides a particularly powerful design tool. Accordingly, requirements for a “more rigid foam like steel” can actually be easily met by simply increasing the relative density of an aluminum foam by a few percentage points.
Actual plots of foam modulus will be found in each foam material section.
Crush strength - There are a number of foam mechanical characteristics, but next to modulus, the most frequently used is the crush strength or plastic yield strength. When a load is applied to a foam structure, it will initially yield elastically in accord with the Young’s modulus equation discussed above. However, at approximately 4-6% of strain, depending on the sample size, the foam structure will begin to buckle and collapse continuously at a relatively constant stress. Depending upon the initial relative density of the foam, this constant collapse will proceed to approximately 50-70% of strain. At that point, the stress / strain curve will begin to rise as the compressed foam enters the “densification” phase. The point in the stress / strain curve where it transitions from the elastic to plastic deformation phase defines the “crush strength” of the foam. This is an important mechanical parameter as it is obviously essential to remain below that level for any structure that is being designed to maintain its shape under design load.
On the other hand, the long, relatively flat section of the curve between the 4-6% transition and 50-70% represents a significant amount of “Work” where Work is defined as = Force × Displacement. This unique characteristic of porous materials makes them very useful as energy absorbers where the kinetic energy of an impacting mass can be absorbed with a controlled load, (represented by the “crush strength”) on the parent support structure.
Given that the crush strength is an important design characteristic in both rigid and collapsible foam structures, it is convenient that the equation that defines the crush strength is nearly as simple and as elegant as that which defines the foam modulus.
Crush Strengthfoam = ~ .58 × Tensile yieldsolid × relative density3/2
Where
Crush strengthfoam = stress at which continuous plastic collapse begins
~ .58 = coefficient to correlate to actual compression data
Tensile yieldsolid = tensile yield of the solid material of the foam struts
Relative density = % relative density in decimal form, i.e. 10% = .1
While similar to the equation for modulus, there are a few issues to be aware of.
1. It may seem counterintuitive that the equation for the compressive or crush strength of a foam structure contains the tensile yield strength of the solid. This is because the foam structure actually crushes by buckling and plastically bending the “beams” or ligaments of the structure. Plastic beam bending in turn is controlled by the tensile yield strength of the strut material.
2. The crush strength or crush plateau is defined as the stress at which continuous collapse is instigated at a relatively constant stress. There is however, a transition zone between the elastic yield and the plastic yield that must be monitored. Any rigid design needs to remain below it, and any energy absorber must remain above it.
3. The coefficient ~.58 is somewhat of a catch-all term that addresses both legitimate technical inputs in the equation and unknown variables such as the assumed yield strength for the solid material. (See summary below).
4. Tensile yieldsolid is the normal mechanical parameter for the solid material of the struts. While this data is readily available for most foam materials, the data is not always exactly applicable as it is typically derived from ASTM standard tensile test specimens that are relatively large in diameter compared to the .004” to .010” diameter ligaments common in foam structures. It is known that tensile test specimen sizes are established to avoid variations due to crystal sizes and other small-scale variables; hence it should not be surprising that the small strut diameters of foams will be subject to these variables. It is therefore essential that caution be used when applying these equations. For example, when designing energy absorbers where the crush strength must be accurately known, initial design can be done using the equations, but final design should be determined by examining actual foam crush test data (see foam material sections) where the foam samples have been manufactured and heat treated in a manner identical to the intended product. As noted in item 3 above, the coefficient is usually adjusted as necessary to compensate for such unknowns.
Summary of foam properties - While there are a variety of other foam characteristics, the ones presented above can address a large number of initial design concepts. One of the most important things to consider when examining foam design issues is that the three foam parameters: pore size, relative density, and foam material, are independent variables, and thus provide a three-dimensional foam design space. Of equal importance is that many of the foam characteristics are functions of only one of these independent variables. Accordingly, it is quite possible to use a single material, let us say a 6000 series alloy aluminum, and create one foam that is 5 pore per inch and 15% relative density in the T-6 heat treat. This will provide a foam material with very low fluid flow pressure drop combined with very high stiffness and strength of about 1000 PSI. On the other hand, the same aluminum material can be foamed to a 40 pore per inch, 4% relative density annealed condition. This will produce foam with high pressure drop and a compression strength around 10-20 PSI. With the additional variation of alternate raw materials, it is obvious that foam materials with a very wide range of characteristics can be readily produced within the three-dimensional design space.
Due to the complexity of some of these characteristics such as crush strength, it is best to use the presented data to make the initial determination regarding the basic feasibility of a foam component. At that point, contact ERG and we can confirm the proposed application and rapidly refine the design concept using additional proprietary data and computer models. We have over 40 years of experience in the manufacture of foam materials and the design and production of foam components that we can apply to bring your design concept to fruition as quickly and as cost-effectively as possible.
