Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands Susan M. Mitchell et al.
Susan M. Mitchell
Mary Kay O’Connor Process Safety Center, Department of Chemical Engineering, The Texas
A&M University System, 3122 TAMU, College Station, Texas 77843-3122, USA
Tel: (979) 575-0808, Fax: (979) 458-1493 e-mail: smmitchen@gmail.com, http://psc.che.tamu.edu/
M. Sam Mannan
Mary Kay O’Connor Process Safety Center, Department of Chemical Engineering, The Texas
A&M University System, 3122 TAMU, College Station, Texas 77843-3122, USA
Tel: (979) 862-3985, Fax: (979) 458-1493 e-mail: mannan@tamu.edu, http://psc.che.tamu.edu/
Ramesh Talreja
Department of Aerospace Engineering, Texas A&M University, 3141 TAMU, College Station,
Texas 77843-3141, USA
Tel: (979) 458-3256, Fax: (979) 845-6051 e-mail: talreja@aero.tamu.edu, http://aero.tamu.edu/
Much recent research has focused on developing materials and systems that can resist damage from expected and unexpected operating modes. While this resistance could be in the form of system or material robustness or present due to the system or material’s ability to reverse damage inflicted, the development of such resistant systems aids in protection from unanticipated failure modes.
The development of such resistance or self-healing is particularly appealing for protecting complicated systems due to system designers’ limited knowledge of how system components may interact. While sophisticated riskassessment tools have been developed to aid designers in protecting engineered systems from hazards ranging from equipment failure to terrorist attacks, these tools generally rely on the engineer’s ability to brainstorm all possible failure modes. Therefore, the concept of resilience was explored to aid in the design of systems that are less prone to failures that could result in catastrophic loss of life or property. The concept of resilience incorporates both the idea of a system having strength or robustness but also having flexibility or “give” to allow deviations from expected operation. In developing this concept, it was important to view resilience as an inherent property of systems to allow for a general definition to be proposed as well as correlations to be developed such that resilience can be compared and optimized for different system designs. An example of previous application of resilience as an inherent property can be found in materials science.
Material resilience can be defined as the “extent to which energy may be stored in [a material] by elastic deformation.
1
” The framework and definition of resilience from materials science has been used as an analogy to define system resilience as “the amount of energy a system can store without failure or instability.
2
”
1 © Springer 2007

Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands Susan M. Mitchell et al.
The system resilience concept has been developed by identifying equivalent stress and strain variables for systems based on thermodynamic measures of the system’s energy and exergy. These variables have been used to develop system response curves, which can be used to characterize system resilience similar to how material stress/strain curves are used to characterize material resilience. Variables developed for the assessment of system resilience will be presented along with system characterization curves for pipe and pump systems. The scalability of the resilience framework will be demonstrated by the comparison of individual process equipment results with results from systems composed of multiple pieces of equipment.
It is anticipated that the development of variables and a methodology that can be used to assess the resilience of a wide range of system types will aid in the identification of properties and characteristics that can be exploited in the development of systems which can not only operate under wider operating ranges, but can also help focus future self-healing research by adding to researchers’ understanding of complicated system behavior and identifying desirable shared system properties.
Keywords: System resilience, Exergy, System stress, System strain, Self-Healing
Modern engineered systems must perform for long periods of time in a reliable manner under what can be extreme conditions. Engineers and scientists have many tools to assist them in designing systems that operate under a wide variety of condition types, however when systems deviate from their expected operating ranges, damage or failure can occur. While engineers have many tools available to predict failure modes of systems, due to the complexity of modern systems it is impossible to predict all possible failure modes. Since it is difficult to protect against these unknown failure modes, systems that can inherently resist damage or self-heal if damage occurs are highly desirable.
A concept that could assist scientists and engineers in protecting physical systems from both the expected and unexpected is resilience. The semantic definition of resilience is “the capacity of a stressed body to recover its size especially after compressive stress.
3
” This concept of resilience incorporates both the aspect of a system being strong or robust enough to withstand forces but also the idea of flexibility or “give” to absorb some fluctuations.
In order to develop this idea of system resilience, the term must be defined and how system resilience is manifested in physical systems should be determined. Then, quantitative assessments should be determined such that resilience can be compared and assessed for different physical systems.
Work has only recently begun in the area of physical system resilience, and much of this work is in the concept stage. However, much work has been conducted which aims to develop systems with desirable concepts similar to those embodied by the idea of resilience. While resilience can be found in multiple research fields, the materials science use of resilience is most beneficial due to the fact that resilience can be viewed as an inherent, measurable property of materials. Material resilience also incorporates multiple aspects of physical behavior – it includes the impact of the material’s stiffness in assessing how much force or stress the system can withstand reversibly as well as the material’s flexibility to allow greater energy storage while still remaining in the reversible, elastic behavior region
1
.
2 © Springer 2007

Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands Susan M. Mitchell et al.
Material resilience is “the ability of a material to absorb energy when deformed elastically and to return it when unloaded
6
” or the “extent to which energy may be stored in [a material] by elastic deformation
1
.
”
Resilience can be measured in the form of a modulus of resilience that is the area under the stress-strain curve from the point of zero stress to the yield stress, or the “strain energy per unit volume required to stress the material from zero stress to the yield stress,
σ 6 .
”
Since physical systems are composed of materials, it is possible that the some properties that cause material resilience may also be present in systems. Therefore, the material resilience definition was adapted for use with systems. The use of the material definition will also allow the development of a concept general enough to allow application to a wide variety of physical systems using the same framework.
Materials science defines resilience in terms of how much energy the material can absorb before yielding begins. By the same analogy, system resilience was defined as “ the amount of energy a system can store without failure or instability
2
.” The use of energy in the definition is attractive since energy is a concept applicable to a variety of systems and disciplines.
However, there are some challenges to using the material resilience definition. One important characteristic of material resilience is reversibility. While no process is perfectly reversible by the second law of thermodynamics, when materials are strained within the resilient range, the process is by definition essentially cyclic (the deformation can be reversed when the stress is released
1
.) However, no system is fully cyclic or reversible. All systems contain sources of irreversibility – energy is conserved but entropy is not. All real processes irreversibly dissipate energy such that the starting conditions cannot be re-achieved without additional energy input. This type of irreversibility creates entropy and includes such processes as friction, heat transfer, spontaneous chemical reaction, or current flow across a resistance.
Conventional energy balances do not always capture meaningful information on these irreversible processes. However, the concept of exergy does – exergy analysis yields information about both a system’s energy and entropy performance. Exergy is a measure of the amount of useful work contained within a system and can be defined as follows:
Exergy is the amount of work obtainable when some matter is brought to a state of thermodynamic equilibrium with the common components of the natural surroundings by means of reversible processes, involving interaction only with the abovementioned components of nature
7
.
Exergy depends on a dead state that is generally defined by the temperature (T
0
) and pressure
(P
0
) at ambient conditions. For a flow process that does not involve mixing or chemical reaction, the exergy of the material stream (Ex) can be determined from the stream’s enthalpy
(H) and entropy (S) and the dead state entropy (S
0
) and enthalpy (H
0
) using the following equation
8
.
Ex
=
H
−
H
0
−
T
0
( S
−
S
0
) (1)
3 © Springer 2007

Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands Susan M. Mitchell et al.
The material stress and strain variables allow material resilience to be quantitatively measured while the material stress-strain curve allows the material’s behavior to be easily visualized. It would be desirable to similarly visualize and quantify system resilience using variables and graphs. However, if a characteristic system behavior curve similar to a stress-strain curve is to be created, system stress and strain variables must be defined first.
Material stress dimensions are force per unit area and the variable measures the load applied to the material divided by the area the load acts upon. While the force applied to a material can be applied to one face, or two dimensions of a material, loads applied to a system act upon all three dimensions and thus could be better defined in terms of the volume of the system, V system
. Also, applied loads to a system are better described in terms of energy input to the system, E in
. Thus, the system stress ( Ss ) was be defined as:
Ss
=
E in
/ V system
(2)
Material strain is non-dimensional – the extensional (or normal) strain measures the change in length of a material element normalized by its initial length. There is no similar, concise variable to measure the deformation of a system. Thus, the source of the deformation will be investigated. Systems deform due to the applied load, or, equivalently, by input of energy.
However, not all energy within the system has the potential to cause deformation. Only the portion of the energy that has potential to do work on the surroundings or the system itself can cause deformation. A ratio of this energy portion, the system’s exergy, can be used to measure the strain of the system. System strain ( Sn ) was defined as the following non-dimensional ratio of exergy destroyed by the system, Ex destroyed
, and the exergy input into the system, Ex in
.
Sn
=
Ex destroyed
/ Ex in
(3)
Using these system stress and strain variables, a characteristic system curve was created by graphing system stress versus system strain. “Stresses” were applied to the system by changing input variables such as flow rate and temperature. Two systems were chosen as test cases to allow development of actual curves. Energy and exergy balances were performed on a water pipe and a water pump to allow calculation of system stress and strain for each case.
Water was chosen as the process fluid due to the fact that its thermodynamic properties can easily be calculated using steam table data. All calculations were performed in Microsoft
Excel using a steam table plug-in, Water97_v13. The water pipe was assumed to be a 5-inch nominal diameter, schedule 40 carbon steel pipe with a roughness due to light rust. The pipe was assumed to not be insulated and have no fittings for simplicity. The water pump was assumed to be an adiabatic, centrifugal pump with a 5-inch inlet pipe.
4 © Springer 2007

Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands Susan M. Mitchell et al.
Both the water pipe and pump destroy exergy due to friction losses. The water pipe also destroys exergy due to heat losses to the surroundings. The pump destroys exergy due to inefficiency within the motor. An energy and an exergy balance were conducted on both systems – the energy and exergy of all input and output streams were calculated using (among other variables and equations) enthalpy values of the water and the exergy equation previously stated for steady-state flow systems. Figure 1 shows the behavior for a water pipe for an inlet pressure of 50 psia. For each mass flow series (45, 43, 41, 39, and 37 kg/s), the inlet water temperature was varied between 120 and 280 o
F. As can be seen in the graph, each of the mass flow rate curves show a similar shape – an indirect relationship between system stress and system strain with the slope of each curve gradually decreasing as strain increases.
Higher mass flow rate curves begin at slightly higher strain values. The pump characteristic system is shown as Figure 2. The inlet water pressure is approximately 48 psia with a pump head of approximately 120 feet. Again, the five curves are for five different mass flow rates and each curve shows behavior when the inlet water temperature is changed from approximately 120 to 280 o
F. Again, there is an indirect relationship between system stress and system strain, however the water pump curve appears closer to a power-law relationship than to a linear relationship.
Water Pipe
160000
120000
80000
40000 mf=45 kg/s mf=43 kg/s mf=41 kg/s mf=39 kg/s mf=37 kg/s mf=35kg/s
0
0.022
0.024
0.026
0.028
Strain = Ex destroyed
/Ex in
0.03
0.032
Figure 1: Characteristic System Curve for Water Pipe Test Case
Water Pump
55000000
40000000
25000000 mf=45 kg/s mf=43 kg/s mf=41 kg/s mf=39 kg/s mf=37 kg/s mf=35 kg/s
10000000
0 0.05
0.1
0.15
0.2
Strain = Ex destroyed
/Ex in
Figure 2: Characteristic System Curve for Water Pump Test Case
It is important that the methodology works on systems no matter their scale. This was investigated by combining the water pipe and pump cases – the outlet of the water pipe was used as the input to the water pump.
5 © Springer 2007

Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands Susan M. Mitchell et al.
The characteristic curve for this combined system is shown in Figure 3. It can be observed that the curve shape is very similar to the pump curve, however the strain values display a wider range.
160000
120000
80000
40000 mf=45 kg/s mf=43 kg/s mf=41 kg/s mf=39 kg/s mf=37 kg/s mf=35 kg/s
0
0 0.05
0.1
0.15
Strain = Ex destroyed
/Ex in
0.2
Figure 3: Characteristic System Curve for Combined Water Pump and Pipe Test Case
Now that a characteristic system curve has been created, the point or region on the curve that shows departure from resilience or resilient behavior can be identified. For linearly elastic materials, the resilient region is characterized by linear slope – there is a direct, linear relationship between material stress and material strain
1
. However, not all materials are linear elastic and display this linear relationship. Similarly, systems display a wide range of relationships between stress and strain. Therefore, characterizing the resilient behavior of systems will not be as straightforward as identifying a linear slope region and then determining when deviation occurs. The behavior of the resilient regime will differ for different systems and for different starting points to the same system.
It would be desirable to be able to identify the functional relationship between variables for each system. Since data is available for varying stress and strain ranges, a trend-line can be fitted through the data. As shown below, a power-law trend-line was chosen where A and B are correlation parameters.
Sn
=
A ( Ss )
B
(4)
A power law relationship was chosen for the trend-line due its flexibility of fit – power law trend-lines will provide accurate relationships for linear data (B=1), directly related data with an increasing slope trend (B>1), and indirectly related data with a decreasing slope trend (B<-
1). Power law relationships have also been widely used in complex system analysis and have been used to predict relationships between properties governing everything from the connectivity of the Internet to the behavior of forest fires
10
.
6 © Springer 2007

Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands Susan M. Mitchell et al.
If the system stress-strain relationship follows a power-law trend, the use of a best-fit line will introduce little error – i.e. the R
2
value of the power trend-line will be close to one. However, if the system begins to deviate from this expected power law relationship, the R
2
of the trendline will begin to decrease.
Since a resilient system should behave in a predictable manner (additional stress should not cause the system’s behavior to deviate from the expected relationship), the R
2
value to the trend line can be used to determine when the system exits its resilient regime.
Trend-lines were fit to the each mass flow curve shown on the individual and combined system graphs and the system was assumed to deviate from resilient behavior at the stress level where the R
2 value dropped below 0.99. For the water pipe test case, no deviation was detected for the 37 to 45 kg/s mass flow curves. For the 35 kg/s curve, the R
2
value dropped below 0.99 when the temperature was 250 o
F and higher (from a starting value of 120 o
F). It makes intuitive sense that the 35 kg/s case might show a limit range over the higher flow rate cases due to the fact that a pipe designed to operate a higher flow rates is under higher initial stress, thus may exhibit a wider range of acceptable operating conditions. The trend-line for all the pump mass flow curves exhibit excellent fit to the data – all the R
2 values were higher than 0.99.
One test of the use of power-law relationships to determine resilient ranges is the combined system graph. Since the combined system incorporates behavior from both the pipe and the pump, the predicted acceptable resilient range should be smaller than the range for either the pump or the pipe separately. When power-law curves were fit to the mass flow data for the combined system, the fit correlation fell below 0.99 at some point for all of the mass flow curves. These values are shown in the table below, where A and B are the values defining the trend-line equation as shown previously in equation 4. As can be seen from the chart, the temperature range for resilience for the combined system matches the temperature range predicted by the individual water pipe graph for the 35 kg/s mass flow curve. Since the range was not limited by the pump case, it is encouraging that the combined system shows this limiting behavior from the individual pipe system curve. Since neither the pump nor pipe individual systems displayed limiting behavior for the other flow rate curves, the range predicted for the combined system is smaller (or equal) to the individual ranges for all flow rate curves.
Mass
Flow Rate, kg/s
Table 1: Combined System Data
Start
Temp, o
F
Max
Temp, o
F
A B R
2
7 © Springer 2007

Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands Susan M. Mitchell et al.
Additional work on this research topic will focus on the extension of the methodology to other units (heat exchangers and more combined systems) as well as the use of the method in conjunction with process simulators to allow more sophisticated parameter variation and the impact of variable changes on more process variables. Also, power law correlations will be further explored to determine if the actual numerical equations can be of use for predication or comparison of system behavior.
The framing and development of the system resilience concept has been presented along with results from a water pipe, water pump, and combined system cases. The use of thermodynamic tools should allow this methodology to be extended to a variety of systems, not just process units. While work remains to develop the system resilience concept, the method presented shows promise for allowing the analysis of a variety of systems and system sizes using one framework.
ACKNOWLEDGEMENTS
This research was performed while on appointment as a U.S. Department of Homeland Security (DHS) Fellow under the DHS Scholarship and Fellowship Program, a program administered by the Oak Ridge Institute for
Science and Education (ORISE) for DHS through an interagency agreement with the U.S Department of Energy
(DOE). ORISE is managed by Oak Ridge Associated Universities under DOE contract number DE-AC05-
00OR22750. All opinions expressed in this paper are the author's and do not necessarily reflect the policies and views of DHS, DOE, or ORISE.
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