It might seem odd to include mechanical concerns in a text on electrochemical engineering. Experience has taught us that the mechanical design is critical in electrochemical systems. Many times performance difficulties can be traced to poor mechanical design or structural failure. Of course, mechanical engineering of materials is a large field in itself. Here our discussion is restricted to just a few mechanical issues that are relevant to fuel cells. A critical question that you as the engineer must answer is, “What axial load (force applied along the axis of the fuel-cell stack, perpendicular to the planar electrodes) should be applied to the cell stack?” As happens with almost any design decision, this choice involves trade-offs among a number of competing factors. Appendix D reviews some basic concepts of mechanics of materials needed for this section.
Contact Resistance
It is essential that the resistance of electrochemical cells be low for practical use. In the introductory chapters, we discussed many important design factors that affect the cell resistance: the conductivity of the electrolyte, electrode structure, and kinetic parameters to name a few. Now we want to treat the contact resistance between components. Although not electrochemical in nature, it can play a critical role in the performance of the cell. When two surfaces are brought together and the interface between them is examined microscopically, we see that the contact is not perfect (Figure 10.18). In fact, there are generally relatively few points of actual contact. The conductance and resistance of this interface are described by
(10.42)
where p is the contact pressure or what we have called the axial load, and k and β are empirical constants. β has a value between 0.5 and 1. The values of β and k depend on the roughness of the surfaces and the materials of the two components in contact. Figure 10.19 shows an example behavior for smooth and rough surfaces. Note that rough surfaces require a higher axial load to achieve a given resistance. A low axial load results in a high contact resistance. At first, the resistance decreases rapidly with increasing load. However, as the axial load increases further, the reduction in resistance is much smaller. There are disadvantages to high loads, which will be discussed shortly.
Figure 10.18 Microscopic picture of two surfaces mated together.
Figure 10.19 Contact resistance of two mated surfaces.
Although the basic behavior is well described with Equation 10.42, the parameters are best obtained experimentally. Comparable behavior is seen for thermal conductance because of the similarity in the two conduction mechanisms in metals. One additional factor that is particularly relevant for us is corrosion (Chapter 16). Oxidation of the surfaces can have a significant impact on the contact resistance. A nonconducting oxide on a steel surface, for example, can dramatically increase the contact resistance.
Sealing
Another factor to be considered when establishing the axial load of the cell stack is sealing. A detailed examination of seals is beyond the scope of this chapter. Nonetheless, a little reflection should convince you that escape of fuel overboard, leakage between the fuel and oxidant streams, or dripping of water on the ground must be prevented. Three common sealing approaches used in fuel cells are discussed briefly. First, wet seals use controlled porosity to establish a liquid barrier to the transport of gases and are suitable for low-temperature fuel cells—see discussion of capillarity from Chapter 5. Second, materials can be bonded together. The specific material used for bonding depends on temperature and compatibility; examples include epoxies, solders and brazes, as well as glass seals. Third, compression seals use compliant elastomers to account for unevenness in the surfaces. These seals can also mitigate the effect of tolerance stack-up, which is the cumulative effect of stacking imperfect parts whose dimensions are within specified tolerances. For example, if cells that are slightly thinner on one side, but within tolerances, are stacked, a bowed cell stack would result if all of the thinner sides were oriented the same way.
We would like to have the axial load high enough so that the contact resistance is small and effective sealing is achieved. The pressure cannot be so high that plastic deformation takes place, resulting in mechanical failure of the stack. Even below this point, the stack can experience failure due to creep, which is discussed later in the chapter. There are numerous methods of applying compressive load. These methods are not only intended to provide the initial axial load, but also to maintain that load over the course of extended operation and through changes in temperature. The most common method uses rigid end plates held together with tie-rods, as explored in Illustration 10.8.
ILLUSTRATION 10.8
One method of applying a compressive load to a cell stack is to use a stiff endplate with tie-rods external to the stack to apply a compressive force. A tie-rod is nothing more than a metal shaft that joins the two end plates. It has been determined that the required force per unit of cell area is 340 kPa. The cell area is 0.1 m2. There are 6 tie-rods with a diameter of 3 mm made from carbon steel. Calculate the stress and strain on the tie-rods.
From the axial load, the force per tie-rod can be calculated and converted to a stress:
which is well below the yield strength of steel, 250 GPa. Using Young’s modulus for steel, 200 GPa, the strain is
Note that the elongation of the rods is simply if the height of the stack is L = 0.5 m.
Illustration 10.9 examines the load (axial stress) needed to compress elements of the fuel-cell stack.
ILLUSTRATION 10.9
An MEA (membrane electrode assembly) for a PEM fuel cell consists of a membrane coated with catalyst on both sides and two gas-diffusion layers (GDLs). See Figure 10.4. Initially, the membrane is 50 μm thick and each of the two gas diffusion layers is 200 μm thick. What stress is needed to compress these layers from 450 to 445 μm? Assume the materials behave elastically, EGDL = 17.1 MPa, Emem = 1.0 GPa.
Under load, the stress, σ, in each component is the same. The final compressed thickness for each component is
and the overall thickness is
Solving for the stress gives σ = 213 kPa.
Stress Induced by Temperature Changes
Materials expand when the temperature is raised. The amount of change depends on the material and is quantified by the coefficient of thermal expansion (CTE) (see Appendix D). Thus, a stress is created in a material if it is constrained and the temperature changed from the stress-free state. In our rudimentary analysis of thermally induced stress in a fuel-cell stack, we will assume that one of the components is much stiffer than the other. Think of stiffness as the ability of the component to resist deformation. This assumption means that the deformation of one component is insignificant relative to that of the other. Stiffness is not simply a material property, but is affected by the thickness and shape of the component. For an anode-supported electrode of an SOFC, for instance, the thickness of the anode material may be much greater than that of the separator. In this case, we assume that the strain of the support is determined from the temperature change, and it remains free of stress. The stress generated in the other component is related to the difference in CTE of the two materials.
(10.43)
where the subscript s refers to the support material, the subscript i refers to the material of interest, νi is Poisson’s ratio, and T0 is the stress-free temperature. This highly simplified analysis will give the engineer a starting point for understanding the importance of matching thermal coefficients of expansion. Most often, the materials are bonded together at high temperature, and this would be the stress-free condition.
What makes thermal expansion of particular importance for SOFCs is the high temperature associated with operation of the fuel cell. A failure mode of importance is fracture, where a material or object separates into two pieces under a mechanical stress. This process is nearly instantaneous and usually catastrophic. This mechanism is of most interest for high temperature cells that use ceramics. The principle of maximum stress applies to brittle materials such as ceramics. If the principal stress reaches its maximum value, the material fractures. This challenge is shown in Illustration 10.10.
ILLUSTRATION 10.10
An anode-supported SOFC is bonded together at 1000 °C. What is the stress in the YSZ separator when cooled to room temperature? The modulus for YSZ is 215 GPa and the coefficients for thermal expansion are 10.5 × 10−6 and 9 × 10−6 K−1 for the support and YSZ separator, respectively. Assume that, because of the thickness of the anode, it is rigid as discussed above. Using Equation 10.43,
where 0.22 is the Poisson’s ratio for the YSZ separator from Appendix D. This stress value is close to the fracture strength of the material (416 MPa), and the design would likely be unacceptable.
The above illustration highlights the challenge associated with operation of high-temperature fuel cells. Brittle fracture is not common in low-temperature systems, but a loss of load can occur in such systems with only relatively modest changes in temperature. This situation arises because the CTE for the cell stack materials is often different from the CTE of the materials used in the loading system. Thus, there is a tendency for the axial load to change significantly with temperature.
ILLUSTRATION 10.11
Using the compressive force from Illustration 10.8, determine the torque on each tie-rod. There is a simple relationship between the torque and the force applied by the tie-rod. Taking c = 0.2,
Six tie-rods are used, each of diameter D. If this torque is applied at room temperature, what would you expect to happen to the compressive force on the stack when the system is heated to 150 °C?
To address this question, we need to consider the expansion of the stack and the expansion of the loading system. If the CTEs are the same and the moduli don’t change with temperature, then there would be no effect. Our load system is made from steel, and the coefficient of thermal expansion for the steel is 10.8 × 10−6 K−1. Therefore, the length would increase from 0.5 m by
The CTE for the stack is 4 × 10−6 K−1; thus, it expands by 0.25 mm. Since the increase in the stack length is less than that of the load system, which is very common, the compressive force will be reduced. To get a quantitative value for the stress at temperature, the specifics of the load system must be considered.
Creep
Below a certain level of stress, the deformation is reversible or elastic; above this stress level, the deformation is permanent. The stress beyond which the deformation becomes plastic is the yield point. Design conditions should not exceed the yield point of the materials. Another mechanism of failure is creep: the permanent deformation of a material subjected to mechanical stress below its yield point. Yielding can occur at stresses below the yield point if stresses are applied for a sufficiently long time or at elevated temperatures. Unlike fracture, creep is a slow process. Furthermore, some creep is generally acceptable as long as it is anticipated and compensated for in the design.
ILLUSTRATION 10.12
For the stack from Illustration , what impact will there be on the compressive load if, due to long-term creep, the cell components permanently deform by 1 mm? Show how this reduction in load is mitigated by using Belleville washers (see Appendix D) for load follow-up.
The stress-free height of the stack is 0.5 m. Using a modulus of 100 MPa for the stack material, we can calculate the compressed length as a function of compressive load assuming elastic compression.
which is depicted with the solid line labeled stack. Point A is the nominal design point. To understand the effect of creep, the effect of the load system must be known. The tie-rods are in tension, and their length increases with stack stress. The slope of the line is
where the length of the expanded tie-rods must equal the compressed thickness of the stack at the design stress. The modulus of the tie-rod material is 50 GPa. The line labeled load system represents this response and intersects with the stack curve at the design point A. Permanent deformation of the stack results in a new curve for the stack with creep, where the zero-stress thickness is now 0.499 m. The intersection of this new curve with the load system, B, becomes the new operating point. Here, we see that the compressive load has been reduced from 340 to about 250 kPa, low enough that cell performance may be adversely affected.
Belleville washers (Appendix D) are basically springs that, when added to the end of the tie-rods, reduce the effective modulus of the tie-rods and make the load system less sensitive to changes in the stack length. This is consistent with your intuition that tells you that the use of springs will help to maintain compression on the stack by helping to compensate for the effect of creep. The curve on the plot was made using an effective modulus of 100 MPa for the load system containing the Belleville washers. For the same creep, the compressive load is now 310 kPa.
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