Design and Analysis of Composite Structures the part.This results in laminates where stiffness and strength are a function of location and provides an added means for optimization [4,5]. Automated fiber placement is most efficient when making large parts.Parts such as stringers, fittings,small frames,that do not have at least one sizeable side where the advantage of the high lay-down rate of material by the robotic head can be brought to bear,are hard to make and/or not cost competitive.In addition,skins with large amounts of taper and number of cutouts may also not be amenable to this process. In addition to the above processes that apply to almost any type of part(with some exceptions already mentioned for automated fiber placement)specialized processes that are very efficient for the fabrication of specific types parts or classes of parts have been developed.The most common of these are filament winding,pultrusion,and press molding using long discontinuous fibers and sheet molding compounds. Filament winding,as already mentioned is the precursor to advanced fiber or tow placement.It is used to make pressure vessels and parts that can be wound on a convex mandrel.The use of a convex mandrel is necessary in order to maintain tension on the filaments being wound.The filaments are drawn from a spool without resin and are driven through a resin bath before they are wound around the mandrel.Due to the fact that tension must be maintained on the filaments,their paths can only be geodetic paths on the surface of the part being woven.This means that,for a cylindrical part,if the direction parallel to the cylinder axis is denoted as the zero direction,winding angles between 15 and 30 are hard to maintain (filaments tend to slide)and angles less than 15 cannot be wound at all.Thus,for a cylindrical part with conical closeouts at its ends,it is impossible to include 0 fibers using filament winding.0 plies can be added by hand if necessary at a significant increase in cost.Since the material can be dispensed at high rates,filament winding is an efficient and low-cost process In addition,fibers and matrix are used separately and the raw material cost is low.Material scrap is very low. Pultrusion is a process where fibers are pulled through a resin bath and then through a heated die that gives the final shape.It is used for making long constant-cross-section parts such as stringers and stiffeners.Large cross-sections,measuring more than 25 x 25 cm are hard to make.Also,because fibers are pulled,if the pulling direction is denoted by 0,it is not possible to obtain layups with angles greater than 45(or more negative than-45).Some recent attempts have shown it is possible to obtain longitudinal structures with some taper.The process is very low cost.Long parts can be made and then cut at the desired length.Material scrap is minimal. With press molding it is possible to create small three-dimensional parts such as fittings. Typically,composite fittings made with hand layup or RTM without stitching suffer from low out-of-plane strength.There is at least one plane without any fibers crossing it and thus only the resin provides strength perpendicular to that plane.Since the resin strength is very low,the overall performance of the fitting is compromised.This is the reason some RTM parts are stitched.Press molding(Figure 2.6)provides an alternative with improved out-of- plane properties.The out-of-plane properties are not as good as those of a stitched RTM structure,but better than hand laid-up parts and the low cost of the process makes them very attractive for certain applications.The raw material is essentially a slurry of randomly oriented long discontinuous fibers in the form of chips.High pressure applied during cure forces the chips to completely cover the tool cavity.Their random orientation is,for the most part,maintained.As a result,there are chips in every direction with fibers providing
the part. This results in laminates where stiffness and strength are a function of location and provides an added means for optimization [4, 5]. Automated fiber placement is most efficient when making large parts. Parts such as stringers, fittings, small frames, that do not have at least one sizeable side where the advantage of the high lay-down rate of material by the robotic head can be brought to bear, are hard to make and/or not cost competitive. In addition, skins with large amounts of taper and number of cutouts may also not be amenable to this process. In addition to the above processes that apply to almost any type of part (with some exceptions already mentioned for automated fiber placement) specialized processes that are very efficient for the fabrication of specific types parts or classes of parts have been developed. The most common of these are filament winding, pultrusion, and press molding using long discontinuous fibers and sheet molding compounds. Filament winding, as already mentioned is the precursor to advanced fiber or tow placement. It is used to make pressure vessels and parts that can be wound on a convex mandrel. The use of a convex mandrel is necessary in order to maintain tension on the filaments being wound. The filaments are drawn from a spool without resin and are driven through a resin bath before they are wound around the mandrel. Due to the fact that tension must be maintained on the filaments, their paths can only be geodetic paths on the surface of the part being woven. This means that, for a cylindrical part, if the direction parallel to the cylinder axis is denoted as the zero direction, winding angles between 15 and 30 are hard to maintain (filaments tend to slide) and angles less than 15 cannot be wound at all. Thus, for a cylindrical part with conical closeouts at its ends, it is impossible to include 0 fibers using filament winding. 0 plies can be added by hand if necessary at a significant increase in cost. Since the material can be dispensed at high rates, filament winding is an efficient and low-cost process. In addition, fibers and matrix are used separately and the raw material cost is low. Material scrap is very low. Pultrusion is a process where fibers are pulled through a resin bath and then through a heated die that gives the final shape. It is used for making long constant-cross-section parts such as stringers and stiffeners. Large cross-sections, measuring more than 25 25 cm are hard to make. Also, because fibers are pulled, if the pulling direction is denoted by 0, it is not possible to obtain layups with angles greater than 45 (or more negative than – 45). Some recent attempts have shown it is possible to obtain longitudinal structures with some taper. The process is very low cost. Long parts can be made and then cut at the desired length. Material scrap is minimal. With press molding it is possible to create small three-dimensional parts such as fittings. Typically, composite fittings made with hand layup or RTM without stitching suffer from low out-of-plane strength. There is at least one plane without any fibers crossing it and thus only the resin provides strength perpendicular to that plane. Since the resin strength is very low, the overall performance of the fitting is compromised. This is the reason some RTM parts are stitched. Press molding (Figure 2.6) provides an alternative with improved out-ofplane properties. The out-of-plane properties are not as good as those of a stitched RTM structure, but better than hand laid-up parts and the low cost of the process makes them very attractive for certain applications. The raw material is essentially a slurry of randomly oriented long discontinuous fibers in the form of chips. High pressure applied during cure forces the chips to completely cover the tool cavity. Their random orientation is, for the most part, maintained. As a result, there are chips in every direction with fibers providing 14 Design and Analysis of Composite Structures
Cost of Composites:a Qualitative Discussion 15 Figure 2.6 Portion of a composite fitting made by press molding extra strength.Besides three-dimensional fittings,the process is also very efficient and reliable for making clips and shear ties.Material scrap is minimal.The size of the parts to be made is limited by the press size and the tool cost.If there are enough parts to be made, the high tooling cost is offset by the low recurring cost. There are other fabrication methods or variations within a fabrication process that specialize in certain types of parts and/or part sizes.The ones mentioned above are the most representa- tive.There is one more aspect that should be mentioned briefly;the effect of learning curves.Each fabrication method has its own learning curve which is specific to the process, the factory and equipment used,and the skill level of the personnel involved.The learning curve describes how the recurring cost for making the same part multiple times decreases as a function of the number of parts.It reflects the fact that the process is streamlined and people find more efficient ways to do the same task.Learning curves are important when comparing alternate fabrication processes.A process with a steep learning curve can start with a high unit cost but,after a sufficiently large number of parts,can yield unit costs much lower than another process,which starts with lower unit cost,but has shallower learning curve.As a result,the first process may result in lower average cost(total cost over all units divided by the number of units) than the first. As a rule,fabrication processes with little or no automation have steeper learning curves and start with higher unit cost.This is because an automated process has fixed throughput rates while human labor can be streamlined and become more efficient over time as the skills of the people involved improve and ways of speeding up some of the process steps used in making the same part are found.The hand layup process would fall in this category with,typically,an 85%learning curve.An 85%learning curve means that the cost of unit 2n is 85%of the cost of unit n.Fabrication processes involving a lot of automation have shallower learning curves and start at lower unit cost.One such example is the automated fiber/tow placement process with, typically,a 92%learning curve.A discussion of some of these effects and the associated tradeoffs can be found in [3]. An example comparing a labor intensive process with 85%learning curve and cost of unit one 40%higher than an automated fabrication process with 92%learning curve,is given here to highlight some of the issues that are part of the design phase,in particular at early stages when the fabrication process or processes have not been finalized yet
extra strength. Besides three-dimensional fittings, the process is also very efficient and reliable for making clips and shear ties. Material scrap is minimal. The size of the parts to be made is limited by the press size and the tool cost. If there are enough parts to be made, the high tooling cost is offset by the low recurring cost. There are other fabrication methods or variations within a fabrication process that specialize in certain types of parts and/or part sizes. The ones mentioned above are the most representative. There is one more aspect that should be mentioned briefly; the effect of learning curves. Each fabrication method has its own learning curve which is specific to the process, the factory and equipment used, and the skill level of the personnel involved. The learning curve describes how the recurring cost for making the same part multiple times decreases as a function of the number of parts. It reflects the fact that the process is streamlined and people find more efficient ways to do the same task. Learning curves are important when comparing alternate fabrication processes. A process with a steep learning curve can start with a high unit cost but, after a sufficiently large number of parts, can yield unit costs much lower than another process, which starts with lower unit cost, but has shallower learning curve. As a result, the first process may result in lower average cost (total cost over all units divided by the number of units) than the first. As a rule, fabrication processes with little or no automation have steeper learning curves and start with higher unit cost. This is because an automated process has fixed throughput rates while human labor can be streamlined and become more efficient over time as the skills of the people involved improve and ways of speeding up some of the process steps used in making the same part are found. The hand layup process would fall in this category with, typically, an 85% learning curve. An 85% learning curve means that the cost of unit 2n is 85% of the cost of unit n. Fabrication processes involving a lot of automation have shallower learning curves and start at lower unit cost. One such example is the automated fiber/tow placement process with, typically, a 92% learning curve. A discussion of some of these effects and the associated tradeoffs can be found in [3]. An example comparing a labor intensive process with 85% learning curve and cost of unit one 40% higher than an automated fabrication process with 92% learning curve, is given here to highlight some of the issues that are part of the design phase, in particular at early stages when the fabrication process or processes have not been finalized yet. Figure 2.6 Portion of a composite fitting made by press molding Cost of Composites: a Qualitative Discussion 15
16 Design and Analysis of Composite Structures Assuming identical units,the cost of unit n,C(n),is assumed to be given by a power law: C(n)=C(1) (2.1) where C(1)is the cost of unit 1 and r is an exponent that is a function of the fabrication process, factory capabilities,personnel skill etc. If p is the learning curve corresponding to the specific process,then C(2n) (2.2) C(n) Using Equation (2.1)to substitute in(2.2)and solving for r,it can be shown that, =器 (2.3) For our example,with process A having PA=0.85 and process B having Pe=0.92, substituting in Equation (2.3)gives rA=0.2345 and rB=0.1203.If the cost of unit 1 of process B is normalized to 1,CB(1)=1,then the cost of unit 1 of process A will be 1.4, based on our assumption stated earlier,so CA(1)=1.4.Putting it all together, 1.4 CA(n)=- n0.2345 (2.4) 1 CBm）=02o (2.5) The cost as a function of n for each of the two processes can now be plotted in Figure 2.7. A logarithmic scale is used on the x axis to better show the differences between the two curves. It can be seen from Figure 2.7 that a little after the 20th part,the unit cost of process A becomes less than that of process B suggesting that for sufficiently large runs,process A may be competitive with process B.To investigate this further,the average cost over a production run of N units is needed.If N is large enough,the average cost can be accurately approximated by: 0.9 0.8 0.7 0.6 Process B 0.5 0.4 ProcessA 0.3 0.2 0.1目 0 10 100 1000 Production run,N Figure 2.7 Unit recurring cost for a process with no automation(process A)and an automated process (process B)
Assuming identical units, the cost of unit n, C(n), is assumed to be given by a power law: CðnÞ ¼ Cð1Þ nr ð2:1Þ where C(1) is the cost of unit 1 and ris an exponent that is a function of the fabrication process, factory capabilities, personnel skill etc. If p % is the learning curve corresponding to the specific process, then p ¼ Cð2nÞ CðnÞ ð2:2Þ Using Equation (2.1) to substitute in (2.2) and solving for r, it can be shown that, r ¼ ln p ln 2 ð2:3Þ For our example, with process A having pA ¼ 0.85 and process B having pB ¼ 0.92, substituting in Equation (2.3) gives rA ¼ 0.2345 and rB ¼ 0.1203. If the cost of unit 1 of process B is normalized to 1, CB(1) ¼ 1, then the cost of unit 1 of process A will be 1.4, based on our assumption stated earlier, so CA(1) ¼ 1.4. Putting it all together, CAðnÞ ¼ 1:4 n0:2345 ð2:4Þ CBðnÞ ¼ 1 n0:1203 ð2:5Þ The cost as a function of n for each of the two processes can now be plotted in Figure 2.7. A logarithmic scale is used on the x axis to better show the differences between the two curves. It can be seen from Figure 2.7 that a little after the 20th part, the unit cost of process A becomes less than that of process B suggesting that for sufficiently large runs, process A may be competitive with process B. To investigate this further, the average cost over a production run of N units is needed. If N is large enough, the average cost can be accurately approximated by: 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10 100 1000 Production run, N Average cost Process B Process A Figure 2.7 Unit recurring cost for a process with no automation (process A) and an automated process (process B) 16 Design and Analysis of Composite Structures
Cost of Composites:a Qualitative Discussion 17 Cm≈N】 C(n)dn (2.6) and using Equation (2.1), j四-(-) N (2.7) Note that to derive Equation(2.7)the summation was approximated by an integral.This gives accurate results for N>30.For smaller production runs (N<30)the summation in Equation (2.6)should be used.Equation(2.7)is used to determine the average cost for Process A and Process B as a function of the size of the production run N.The results are shown in Figure 2.8. As can be seen from Figure 2.8,Process B,with automation,has lower average cost as long as less than approximately 55 parts are made (N<55).For N>55,the steeper learning curve of Process A leads to lower average cost for that process.Based on these results,the less-automated process should be preferred for production runs with more than 50-60 parts.However,these results should be viewed only as preliminary,as additional factors that play a role were neglected in the above discussion.Some of these factors are briefly discussed below. Process A,which has no automation,is prone to human errors.This means that:(a)the part consistency will vary more than in Process B;and(b)the quality and accuracy may not always be satisfactory requiring repairs,or scrapping of parts.In addition,process improvements, which the equations presented assume to be continuous and permanent,are not always possible.It is likely that after a certain number of parts,all possible improvements have been implemented.This would suggest that the learning curves typically reach a plateau after a while and cost cannot be reduced below that plateau without major changes in the process(new equipment,new process steps,etc.).These drastic changes are more likely in automated processes where new equipment is developed regularly than in a nonautomated process. 1.4 1.2 Process A 1 0.8 0.6 Process B 0.4 0.2 10 100 1000 Unit number,n Figure 2.8 Average recurring cost for a process with no automation(process A)and a fully automated process (process B)
Cav ¼ 1 N X N n¼1 CðnÞ 1 N ð N 1 CðnÞdn ð2:6Þ and using Equation (2.1), Cav ¼ 1 N ð N 1 Cð1Þ nr dn ¼ Cð1Þ 1r 1 Nr 1 N ð2:7Þ Note that to derive Equation (2.7) the summation was approximated by an integral. This gives accurate results for N > 30. For smaller production runs (N< 30) the summation in Equation (2.6) should be used. Equation (2.7) is used to determine the average cost for Process A and Process B as a function of the size of the production run N. The results are shown in Figure 2.8. As can be seen from Figure 2.8, Process B, with automation, has lower average cost as long as less than approximately 55 parts are made (N < 55). For N > 55, the steeper learning curve of Process A leads to lower average cost for that process. Based on these results, the less-automated process should be preferred for production runs with more than 50–60 parts. However, these results should be viewed only as preliminary, as additional factors that play a role were neglected in the above discussion. Some of these factors are briefly discussed below. Process A, which has no automation, is prone to human errors. This means that: (a) the part consistency will vary more than in Process B; and (b) the quality and accuracy may not always be satisfactory requiring repairs, or scrapping of parts. In addition, process improvements, which the equations presented assume to be continuous and permanent, are not always possible. It is likely that after a certain number of parts, all possible improvements have been implemented. This would suggest that the learning curves typically reach a plateau after a while and cost cannot be reduced below that plateau without major changes in the process (new equipment, new process steps, etc.). These drastic changes are more likely in automated processes where new equipment is developed regularly than in a nonautomated process. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1 10 100 1000 Unit number, n Normalized cost Process A Process B Figure 2.8 Average recurring cost for a process with no automation (process A) and a fully automated process (process B) Cost of Composites: a Qualitative Discussion 17
18 Design and Analysis of Composite Structures Therefore,while the conclusion that a less-automated process will give lower average cost over a sufficiently large production run,is valid,in reality may only occur under very special circumstances favoring continuous process improvement,consistent high part quality and part accuracy,etc.In general,automated processes are preferred because of their quality,consis- tency,and potential for continuous improvement. The above is a very brief reference to some of the major composite fabrication processes.It serves to bring some aspects to the forefront as they relate to design decisions.More in-depth discussion of some of these processes and how they relate to design of composite parts can be found in[6,7刀]. 2.2 Nonrecurring Cost The main components of nonrecurring cost follow the phases of the development of a program and are the following. Design.Typically divided in stages (for example,conceptual,preliminary,and detail)it is the phase of creating the geometry of the various parts and coming up with the material(s)and fabrication processes (see Sections 5.1.1 and 5.1.2 for a more detailed discussion).For composites it is more involved than for metals because it includes detailed definition of each ply in a layup (material,orientation,location of boundaries,etc.).The design of press-molded parts would take less time than other fabrication processes as definition of the boundaries of each ply is not needed.Material under pressure fills the mold cavity and the concept of a ply is more loosely used. Analysis.In parallel with the design effort,it determines applied loads for each part and comes up with the stacking sequence and geometry to meet the static and cyclic loads without failure and with minimum weight and cost.The multitude of failure modes specific to composites(delamination,matrix failure,fiber failure,etc.)makes this an involved process that may require special analytical tools and modeling approaches. Tooling.This includes the design and fabrication of the entire tool string needed to produce the parts:Molds,assembly jigs and fixtures etc.For composite parts cured in the autoclave, extra care must be exercised to account for thermal coefficient mismatch(when metal tools are used)and spring-back phenomena where parts removed from the tools after cure tend to deform slightly to release some residual thermal and cure stresses.Special (and expensive) metal alloys (e.g.Invar)with low coefficients of thermal expansion can be used where dimensional tolerances are critical.Also careful planning of how heat is transmitted to the parts during cure for more uniform temperature distribution and curing is required.All these add to the cost,making tooling one of the biggest elements of the nonrecurring cost.In particular,if matched metal tooling is used,such as for RTM parts or press-molded parts,the cost can be prohibitive for short production runs.In such cases an attempt is made to combine as many parts as possible in a single co-cured component.An idea of tool complexity when local details of a wing-skin are accommodated accurately is shown in Figure 2.9. Nonrecurring fabrication.This does not include routine fabrication during production that is part of the recurring cost.It includes:(a)one-off parts made to toolproof the tooling concepts; (b)test specimens to verify analysis and design and provide the data base needed to support design and analysis;and(c)producibility specimens to verify the fabrication approach and avoid surprises during production.This can be costly when large co-cured structures are involved with
Therefore, while the conclusion that a less-automated process will give lower average cost over a sufficiently large production run, is valid, in reality may only occur under very special circumstances favoring continuous process improvement, consistent high part quality and part accuracy, etc. In general, automated processes are preferred because of their quality, consistency, and potential for continuous improvement. The above is a very brief reference to some of the major composite fabrication processes. It serves to bring some aspects to the forefront as they relate to design decisions. More in-depth discussion of some of these processes and how they relate to design of composite parts can be found in [6, 7]. 2.2 Nonrecurring Cost The main components of nonrecurring cost follow the phases of the development of a program and are the following. Design. Typically divided in stages (for example, conceptual, preliminary, and detail) it is the phase of creating the geometry of the various parts and coming up with the material(s) and fabrication processes (see Sections 5.1.1 and 5.1.2 for a more detailed discussion). For composites it is more involved than for metals because it includes detailed definition of each ply in a layup (material, orientation, location of boundaries, etc.). The design of press-molded parts would take less time than other fabrication processes as definition of the boundaries of each ply is not needed. Material under pressure fills the mold cavity and the concept of a ply is more loosely used. Analysis. In parallel with the design effort, it determines applied loads for each part and comes up with the stacking sequence and geometry to meet the static and cyclic loads without failure and with minimum weight and cost. The multitude of failure modes specific to composites (delamination, matrix failure, fiber failure, etc.) makes this an involved process that may require special analytical tools and modeling approaches. Tooling. This includes the design and fabrication of the entire tool string needed to produce the parts: Molds, assembly jigs and fixtures etc. For composite parts cured in the autoclave, extra care must be exercised to account for thermal coefficient mismatch (when metal tools are used) and spring-back phenomena where parts removed from the tools after cure tend to deform slightly to release some residual thermal and cure stresses. Special (and expensive) metal alloys (e.g. Invar) with low coefficients of thermal expansion can be used where dimensional tolerances are critical. Also careful planning of how heat is transmitted to the parts during cure for more uniform temperature distribution and curing is required. All these add to the cost, making tooling one of the biggest elements of the nonrecurring cost. In particular, if matched metal tooling is used, such as for RTM parts or press-molded parts, the cost can be prohibitive for short production runs. In such cases an attempt is made to combine as many parts as possible in a single co-cured component. An idea of tool complexity when local details of a wing-skin are accommodated accurately is shown in Figure 2.9. Nonrecurring fabrication. This does not include routine fabrication during production that is part of the recurring cost. It includes: (a) one-off parts made to toolproof the tooling concepts; (b) test specimens to verify analysis and design and provide the data base needed to support design and analysis; and (c) producibility specimensto verify the fabrication approach and avoid surprises during production. This can be costly when large co-cured structures are involved with 18 Design and Analysis of Composite Structures