Nontraditional manufacturing (NTM) processes refer to processes in which nontraditional energy transfer mechanism and/or nontraditional media for energy transfer are involved. The project is focused on nontraditional material removal or machining processes. They include electrical discharge and electrochemical machining (EDM/ECM), laser machining processes (LMP), abrasive waterjet machining (AWJM), among others. NTM processes can machine precision components from sophisticated materials. They offer the advantages of a reduced number of machining steps and a higher product quality. NTM can also exist within the realm of automated production. Interest in NTM has been on rise due to increasing interests in the vastly superior properties of innovative materials such as superalloys, composites and ceramics. NTM offers an attractive alternative and often the only choice for the processing of these materials. The new and potential applications require enhanced process capabilities and more precise process design and optimization capabilities. In response, substantial research progress has been made in recent years especially in the areas of process innovation, modeling, simulation, monitoring and control.

Progress has also been made in education of NTM processes. Education at the introductory level has been appropriate. Innovations and more orchestrated efforts, however, are needed at the upper level undergraduate and introductory graduate (ULUIG) curricula. NTM processes are diverse and of many types. They are also multi-disciplinary, involving thermal, fluids, chemical reaction, material science, system design and control theory. To teach research level materials at the ULUIG level, more time and effort are needed to prepare students. With more and more new research results being incorporated into courses with fixed credit hours, teaching efficiency and efficacy need marked improvement. Besides innovations in teaching methodologies, computer aided tools developed in research as well as computer aided teaching technologies offer great opportunities in this endeavor.

The objectives of this project, therefore, are:

1. To develop methodologies and educational materials to incorporate recent research results in NTM processes and systems into ULUIG level curricula
2. To prepare a new generation of engineers who have the analytic background knowledge and process design/optimization skills by using modern tools
3. To establish a national model of effective and efficient learning of multi-disciplinary subjects.

Laser Machining Process (LMP) is one of seven modules of this project.

Laser machining is the material removal process accomplished through laser and target material interactions. Generally speaking, these processes include laser drilling, laser cutting, and laser grooving, marking or scribing.

Laser machining processes transport photon energy into the target material in the form of thermal energy or photochemical energy, they remove material by melting and blow away, or by direct vaporization/ablation. On the other hand, traditional machining processes rely on mechanical stresses induced by tools to break the bonds of materials. This basic difference in material removal mechanism decides the advantages and disadvantages of LMP compared with traditional machining processes.

1. Laser machining is localized, non-contact machining and is almost reacting-force free, while traditional machining usually has direct mechanical contact and need devices to balance the machining force, work piece needs clamping. The forces in laser machining are of micro scale. The photon pressure on target material is negligible for bulk material. This offers LMP flexibility in machining delicate parts where no large mechanical force can be acted on. Another big advantage is that fixtures can be greatly simplified compared with traditional machining.
2. LMP can remove material in very small amount, while traditional machining remove material in macro scale. LMP are said to remove material "Atom by Atom". For this reason, the kerf in laser cutting is usually very narrow, the depth of laser drilling can be controlled to less than one micron per laser pulse and shallow permanent marks can be made with great flexibility. In this way material can be saved, which may be important for precious materials or for delicate structures in micro-fabrications. But this also means small removal rate in LMP compared with traditional machining. Laser machining is not good at bulk material removal through pure thermal effects. The ability of accurate control of material removal makes laser machining an important process in microfabrication and micro-electronics. Also laser cutting of sheet material with thickness less than 20mm can be fast, flexible and of high quality, and large holes or any complex contours can be efficiently made through trepanning.
3. Heat Affected Zone(HAZ) in laser machining is relatively narrow and the re-solidified layer is of micron dimensions. For this reason, the distortion in laser machining is negligible. In traditional machining, large areas of work hardening is almost unavoidable.
4. LMP can be applied to any material that can properly absorb the laser irradiation, while traditional machining processes have to choose suitable tools for materials with different hardness or abrasiveness. It is difficult to machine hard materials or brittle materials such as ceramics using traditional methods, laser is a good choice for solving such difficulties.
5. LMP can achieve final quality level machining results in one process, while in traditional machining several processes are commonly used. Laser cutting edges can be made smooth and clean, no further treatment is necessary. High aspect ratio holes with diameters impossible for other methods can be drilled using lasers. Dross adhesion and edge burr can be avoided, geometry precision can be accurately controlled. The machining quality is in constant progress with the rapid progress in laser technology. Although some traditional machining can achieve higher surface qualities than common LMP, LMP has the potential of nm scale machining. It was reported that laser was used for interactive optics finishing.
6. Small blind holes, grooves, surface texturing and marking can be achieved with high quality using LMP. Traditional machining may be advantageous for macro scale applications, it is usually more economical and efficient to use LMP for micro scale applications.
7. LMP has the potential for more flexibility. Laser light can be transmitted and reflected to the desired locations at high speeds, precise 3D positioning can be conveniently realized. The combination of fiber transmitted laser energy and robots technology can provide a system with great dimensional freedom.
8. Laser machining is sensitive to the focusing property of the laser beam. At the focus the laser intensity is highest, away from it laser intensity drops. The Depth of Focus of the laser beam is relatively small (tens of microns to around a hundred millimeters) , the cutting depth is thus limited due to this factor along with other complexities when the cutting depth increases.
9. Laser technology is in rapid progressing, so do laser machining processes. High power lasers suitable for laser machining are becoming more and more compact, some systems can generate lasers with tunable wavelengths and pulse duration. A quiet, compact but very powerful laser machining system will be used more and more widely!

In summary, laser machining processes are non-contact, flexible and accurate machining processes applicable to a wide range of materials. And they are in rapid developing. In fact laser machining is only a small fraction of laser related applications and all these areas are in rapid development. In this module we will discuss laser machining related topics.

Rapid advance in laser related technology has made more and more applications of lasers in mechanical engineering not only practical, but also efficient, precise, economical and flexible. The applications include Laser Cutting, Laser Grooving, Laser Drilling and Laser Welding, Laser Forming^[4], Laser Cold Cutting, Laser Micromachining^[5], Laser Surface Treating^[1,2], RPM, Rapid Tooling^[3], etc. Progress in laser processing comes along with other technologies which we call "Non-Traditional Manufacturing (NTM)" , such as Abrasive Waterjet Machining, Electrical Discharge Machining, Electrochemical Machining, Ultrasonic Machining, Ion or Plasma Machining, etc. The role of NTM is becoming more and more important in both industry and research.

As we are carrying out this NSF supported NTM research projects, we are impelled to think in depth not only the technical details, but also the philosophy and methodology behind traditional manufacturing, NTM and various new engineering thoughts.

First let's discuss the relation between traditional and nontraditional Manufacturing, then let's see the features of Laser Energy Field from a new viewpoint, finally let's talk about the organization of this module.

3.1 The Relation between Traditional and Non-Traditional Manufacturing ^[14]

Rising production costs dictates that production operations be automated whenever possible; innovative materials such as super-alloys, composites, ceramics and many other advanced materials, which are difficult to or cannot be processed by traditional machining methods, require new manufacturing technologies; environmental considerations require the development of Environmentally Conscious processes. NTM processes are often well suited to be monitored and controlled, the processing steps can be reduced with precision remains high. These are the impetuses for nontraditional manufacturing. In many cases, traditional manufacturing may have reached their capability limits, while NTM are offering the best resolution. But what's the difference between NTM and traditional manufacturing processes?

K. P. Rajurkar et al. Made the following statement^[6]. "NTM processes can be broadly categorized in two ways: (1) processes in which there is a nontraditional mechanism of interaction between the tool and the workpiece, and (2) processes in which nontraditional media are used to effect the transfer of energy from the tool to the workpiece." In contrast, "Traditional Machining relies on direct mechanical contact between the tool and workpiece", which often cause undesired changes in the properties of workpiece, such as residual mechanical and thermal stresses. Figure 1 was used to summarize the common features of NTM. On the top and bottom are the interaction mechanisms and energy carriers or working medium, the energy transfer in a process can be continuous or pulsed, machining area can be local or full.

Figure 1. Generalized conditions diagram for Nontraditional Manufacturing processes (Rajurkar, 1992)

In some sense, traditional means things that are mature and widely accepted for some time. So the content of traditional changes with time. In some cases, the distinction between traditional and nontraditional manufacturing is not so obvious, for example, Abrasive Water-jet Machining uses mainly mechanical interaction, but it is commonly regarded as NTM; many new advances have been made in casting and thermal treating, but they been used for thousands of years.

In fact manufacturing has progressed into a time that many kinds of energy forms and interactions are coupled together, the combination of traditional and nontraditional manufacturing has produced many inspiring results. The strict distinction of traditional and nontraditional is not so important, but it is appropriate to regard mechanical force/energy as a common kind of force/energy, which is parallel to light, sound, electricity etc. Mechanical engineering needs constant innovations to meet various challenges. When we try to uncover the potentials of various manufacturing processes, it is important to purposely and systematically use various energy and energy fields to optimize our engineering solutions.

The essence of manufacturing engineering is utilizing information to control energy and mass to achieve human being's desired objectives. Figure 2 illustrates that three flows exist in any manufacturing processes (P), they are information flow (I), energy flow (E) and mass/material flow (M). The degree of combination or integration of the three flows can be used as index of process optimization^[7].

Figure 2. Three flows in manufacturing processes

One common feature of NTM is the extensive use of various energy forms and energy fields, the whole engineering is in fact the art of energy field utilization and manipulation. Energy field means the distribution of energy or force, it is the area or space where a kind of energy or force can be felt. Some may think we normally use "point energy" which is not energy field, but point is a relative concept, it is localized energy field. A focused laser beam might be regarded as a point energy source, but for micromachining we must consider its spatial and temporal distribution. So energy field is a more general concept. Traditional machining commonly relates to stress field and thermal field, of course, gravitational field and environmental pressure field are always affecting any processes on earth. The more energy fields we consider, the more accurate and flexible can we control our processes.

Any kind of energy fields has its advantages and disadvantages, our aim is to find the best combination for our purposes. In addition to commonly known energy fields, such as mechanical forces, sound, light, electromagnetic and thermal fields, particle flows (such as electron beams, ion flows) and fluid flows, it is convenient to treat medium environment as a special kind of energy field--Medium Field. Medium distribution is regarded as energy field because different medium distributions can affect processing with great differences. Chemical machining and EDM need special medium environment to do their work. Reactive Laser Cutting uses Oxygen to assist cutting ^[8]. Different medium distributions can be defined to be of different energy states. This not only helps explain physical phenomena, but also can help quantify the effects of medium environment. Clever applications of Medium Field can be found in many realms, Lasers, diodes and transistors are such examples. Semiconductor Lasers and Q-Switch pulsed lasers are good examples of medium field, for details please refer ^[9].

3.2 Four Attributes Analysis of Laser Energy Fields

Building up a clear overall physical image first is important when we try to exploit various energy fields. Four Attributes Analysis of laser phenomena is very helpful for our research and modeling, it is useful to other energy fields as well. We will mainly use laser phenomena to illustrate Four Attributes Analysis of Energy Fields.

Velocity, acceleration and feeding rate are part of time attribute. Temporal modulation of energy field has been proved to be an effective way to improve machining quality. We mainly discuss the time scale effects, continuous/discrete effects and the relativity effects of time attribute here.

The temporal distributions of energy fields can be of very different time scales, which can greatly affect the interaction between energy and material.

Heat Affected Zone (HAZ) for pulsed laser processing is usually smaller than that of CW laser processing. More striking phenomena were found when pulsed lasers progressed from ns scale (10^-9 second) to under ps (10^-12 second). For fs (10^-15 second) scale laser processing, radical changes happened: heat affected zone decreased to almost zero at different wavelengths for the same material ^[10]. These were attributed to the ultra-short laser pulse duration. We briefly explain this as following. When laser beam acts on the material, laser energy is first absorbed by electrons. The absorbed energy then propagates through the electron subsystem, then transferred to the lattice. In this way laser energy is transferred to the ambient target material, as illustrated by figure 3. Three characteristic time scales are Te--the electron cooling time, which is in the order of 1ps; Ti-- the lattice heating time; and Tl--t7he duration of laser pulse. Te and Ti are proportional to their heat capacity divided by a same constant, and the heat capacity of electron is much less than that of lattice, so Te<<Ti. Te, Ti are decided by materials, Tl is what we can choose to make a difference. Three cases occur when Tl is in different ranges.

Figure 3. Energy flow in laser-material interaction

Case one: Tl >1 ns >>Ti>>Te. In this case, electron absorbed laser energy has enough time to be transferred to lattice, electron and lattice can reach thermal equilibrium, the main energy loss is the heat conduction into the solid target. Material is first melted, when the beam is strong enough, evaporation occurs from liquid state. The existence of melting layer makes precise material removal using laser pulses above nanosecond very complicated. Case two: Ti>>Te>>Tl, Tl is of fs scale, laser pulse duration is shorter than the electron cooling time. Electrons are heated instantly, then in about 1 ps electrons transfer their energy to their positive lattice ions. When this energy intensity is high enough, which is often true for ultra-fast pulsed lasers, those ions get energy high enough to break the bonding of lattice structure, they break off instantly without having time to transfer their energy to their neighboring lattice ions, thus direct solid-vapor transition occurs. Heat conduction into the target can be neglected, heat affected zone is greatly reduced. For melting-free ablation to be possible, two conditions must be met: ultra-short pulse duration and high enough pulse energy. Case three: Ti >>Tl>>Te, Tl is of ps time scale. This is a transitional situation, melting layer exists in laser ablation.

The temporal distributions of energy fields can be continuous or discrete, both have their advantages and disadvantages relative to their applications, it's bias to think either of them to be better forever, their relation is similar to analog and digital circuits. Both CW lasers and pulsed laser are used widely in laser machining. The interaction between Grinding and multi-threads drilling tools and parts are also discrete. Consider the following example. Usually vibration can do harm to precision in machining, but it is reported that by using ultrasonic pulse cutting, the lathe tools get great instantaneous speed and accelerate in a very short period, high energy is exerted in a very limited area. This process smoothly transforms plastic materials to relatively brittle state, cutting force is decreased, cutting time is shortened, cutting heat is minimized and residual stress is greatly relieved ^[11]. This process solved many otherwise commonly met difficulties by using energy field method--change continuous cutting to discrete micro-cutting, this is a typical example of energy field temporal modulation.

An important time duration effect is that when the energy field intensity and energy pulse duration reach certain extent, something unusual may happen. This doesn't limit to the two examples we gave, this should be an effective way to uncover the potentials of various energy fields. We should also be aware of the relativity of time effects. Relative to very fast events such as very short energy pulses, the event varying at normal speed can be treated as static. Below a corresponding time scale, objects usually demonstrate very abnormal properties. For example, the property of liquid can change for different time scales, below 10^-12 second, water can not be treated as Newtonian fluid anymore.

(B) Spatial Attribute

Spatial distribution of energy field is directly related to energy acting area, acting location and relative position between tool/energy sources and parts.

Laser can be transmitted over long distances with very small divergence, laser beam spot size can vary from 1 m m to 10 mm. Highly focused beams can act locally with high intensity, which are used for precision material removal, defocused laser beams are used for surface treating, laser forming, etc. In laser machining the relative position between laser source and parts is important. Optical fibers have been used in communication for a long time, now they are used to carry high power laser beams in manufacturing, they add valuable flexibility in laser energy transmission. It's the refractive index difference in the fiber system that makes low loss light energy transmission feasible. Waterjet in air forms a natural waveguide system for laser beam, this property has been used in US patent 5292498: Local Laser Plating Apparatus. Spatial adjustments of energy fields are widely used to achieve various objectives. Telescope, microscope, thermal couple are representative examples.

Why are pulse duration time and focus spot size so important in laser processing? It will be clear after we have examined some energy indexes. Peak Power equals pulse energy divided by pulse duration time, Intensity is the area average of peak laser power. When the interaction between energy field and target is not continuous, energy intensity is usually the deciding factor. Let the absolute energy in a laser pulse be 0.1J, fixed. Let pulse lasting time be dT second, let pulse repetition rate be f Hz, and 1/f > dT. Let the beam focused spot size be D cm in diameter. If pulse repetition rate can vary in the range of 1Hz~4kHz, then average power is f*E = 0.1~400W. Let's vary pulse length and acting area, compute the peak power and intensity. We see clearly from the figure below, peak intensity of a 10 fs pulse with D=1 m m is 10²²W/cm², while the intensity of a 1 m s pulse with D=1 mm is10⁷W/cm².

Figure 4. Laser intensity & beam size and pulse duration

(C) Frequency Attributes

Human beings have accumulated plenty of resources relating frequency properties of energy field, we can expect more advanced manufacturing processes to be invented by applying frequency modulation rule. Laser material processing is just one of such examples. The frequency here is the characteristic frequency of energy field, which is different from Pulse Repetition Rate. Radio wave, microwave, sound wave, mechanical vibration, lattice vibration, gas molecule collision, etc., all have their respective characteristic frequencies. Thermal radiation has spectral distribution, many other energy forms or material properties are also related with frequencies. Lasers usually have very narrow spectral width, while other energy forms may have very broad and complex frequency distributions. Some energy field's characteristic frequency is not obvious, such as gravitation field, medium field, thermal energy, stress energy, vacuum field, fluid pressure field etc. Their frequency distributions are either being discovered or are nearly zero.

The characteristic frequency of energy field is important because materials may response very differently to energy fields at different frequencies. UV laser ablation of organic polymers is very different from infrared or visible laser ablation, their ablation mechanisms are very different ^[13]. The infrared and visible laser ablation is mainly photo-thermal degradation, while UV laser ablation involves direct photo-chemical dissociation. The emissivity of copper varies with wavelength as seen in table 1. That's the reason why lasers at different wavelengths are used to process different materials.

Table 1: Spectral emissivity e l of Cu at different wavelength(m m), T=293K, normal to surface^[10]:

The diffraction free focus spot size is proportional to light wavelength. For circular beams, the focal spot size is:

Dmin= 2.44f*l /D

where f is the lens focus length, l is the light wavelength, D is the unfocused beam diameter. This defines the upper limit of laser processing precision at a specific frequency. Thus for high precision applications, short wavelength lasers are preferred.

(D) Amplitude Attributes

Frequency and amplitude are closely related. Amplitude or magnitude is a direct measure of energy field intensity, deciding what amplitude is proper or optimal is our everyday work. For energy field method, we are interested in the effective ways of amplitude modulation and the direct or indirect amplitude effects of various energy fields. In optics, optical filters, polarizers, attenuators, beam expanding and focusing systems are used to modulate laser intensity and spatial distribution. With their help, we can match the laser power output to very different applications in the same time without disturbing the laser source.

A common rule relating the amplitude of energy field is: certain valve value exists for the interaction between material and energy field, below this value, the interaction mechanism may be simple and linear, beyond this value, the mechanism becomes nonlinear, and at extreme conditions, striking abnormal phenomena will happen. This indicates that some kind of transition mechanism between frequency and amplitude exists, or we can say, the effect of amplitude adjustment is somewhat equivalent to the effect of frequency adjustment. An example is self-focusing of laser light. When laser intensity is high enough, media refractive index changes. Usually the higher the intensity, the bigger the refractive index. Since the center of a Gaussian laser beam has higher intensity than the rims, when the beam passes through optical medium, central area has bigger refractive index than the circumferential parts, equivalent lens focusing effect occurs. When we have reached the extreme of normal focusing systems, using this method can further focus the spot to 1/5! Remember machining precision is decided by the smallest spot size achievable, this is equivalent to a new laser source whose wavelength has been reduced to 1/5 of original.

Modulators usually saturate or even burn down at too high magnitude of energy flow. If modulators can only work at low energy level, but we must generate ultrahigh energy flows through them, what shall we do? We can wait until modulators that can withstand the required high energy be produced or we can learn something from ultra-short pulsed lasers. Let's jump over the technical and physical principles details, then we can focus on the general rules inside. Ultrafast laser oscillators generate pulse energy initially at nJ (10^-9J) scale, amplification to mJ level is needed in micromachining, but we know, when pulse lasting time is very small, peak energy intensity goes up far beyond the safety operation range of normal optical amplification systems. Ultrashort pulsed lasers successfully solved this difficulty using Chirped Pulse Amplification (CPA) and Pulse Compression techniques. The energy of ultrafast lasers are highly concentrated in time domain, but their frequency distributions are much broader than normal laser systems. Light at different frequencies travel at different speeds through optical mediums. This is a bad thing at first glance because we normally desire same rules being obeyed by as many objects as possible. Contrary to our intuition, this forms the base for the final solution. Figure 5 illustrates the idea. In free space, different components in a broad band laser pulse travel at nearly same speed, time concentration of the beam is kept. When normal optical components are in the optical path, long wavelength light components travel through the medium faster than short wavelength components, thus pulse lasting time is stretched, energy intensity is lowered. Special optical devices such as chirped mirrors or special prism pairs are used to compensate the pulse spreading, they allow short light components pass through faster than long wavelength components, so they compress pulse lasting time. When stretching and compressing are used together, the solution is there!

Figure 5. Principle of ultrafast laser systems

The enlightenment of this example is: time, space, frequency and amplitude of energy field are interconnected, no property is absolutely positive or negative to our ends, by properly making use of these properties, we can usually circumvent difficulties unavoidable by normal ways.

3.3 Organization of the Module: Laser Machining Processes

The Module will be presented in terms of three broad topics: Energy, System and Material, to reflect the philosophy we have discussed and to facilitate possible coordination with other modules of this project.

Each topic will be presented in three levels: Introductory, Intermediate and Advanced, to suit different needs.

The Introduction level will include the most basic phenomena, mechanisms and theories. Qualitative description will be emphasized and simple quantitative relations may also be included. The purpose is to give an overall basic understanding of LMP. Introductory level is for beginners or those who just want to get a general and basic understanding of the laser machining process. The contents are feature as descriptive and qualitative, mathematics is purposely reduced.

The Intermediate level will include all important phenomena, mechanisms and theories. Quantitative relations will be emphasized and analytical tools will be provided. Some recent research results will be included. This level prepares for in-depth understanding and for advanced research. Intermediate level is aimed to give a relative complete knowledge of the laser machining process. It is self-contained, but some references are made to level one to avoid repetitions. More theoretical aspects of laser machining processes are presented than level one. This level is for upper-level undergraduates and first-year graduates. The contents is systematically organized to make it suitable for self learning, as a text or as a useful references for a university course about laser machining processes.

The Advanced level will include the relatively special phenomena, mechanisms and relatively more advanced theories and analytical tools that primarily target graduate students and researchers. Recent research results will mostly be included here.

These three levels can be taken sequentially or individually. The above structure will be convenient for cross-referencing, especially when it is implemented on the Web. Multimedia techniques are used to make the web different from a paper-textbook: you can click to see the definition of a term, you can jump to any interested link, you can try the interactive relations, etc.

Next let's give a brief review of the contents in the module.

4. Brief review of the contents in this module

References:

[1] Geroge Chryssolouris, "Laser Machining", New, Springer-Verlag, 1991;

[2] William M. Steen, "Laser Material Processing", London, Spring-Verlag, 2^nd Printing 1994;

[3] Yongnian Yan et al., "Progress in Rapid Prototyping Manufacturing and Rapid Tooling", Proceedings of ICRPM'98, Beijing;

[4] Wenchuan Li, Jiangcheng Bao, Y. L. Yao, " Dimensional characteristics and mechanical properties of laser-formed parts", High Temperature Material Processes, invited paper;

[5] X. Liu, D. Du and G. Mourou, "Laser Ablation and Micromachining with Ultrashort Laser Pulses", IEEE Journal of Quantu Electronics, Vol. 33, NO. 10, Oct., 1997, p1706-1716;

[6] K.P. Rajurkar et al., "The Role of Nontraditional Manufacturing in Future Manufacturing Industries", P23, Manufacturing International 1992;

[7] Feng Lin, "Research on the Principle of Slicing Solid Manufacturing Process and The System Development", doctor dissertation of Tsinghua University 1997, China, P73;

[8] William M. Steen, "Laser Material Processing", London, Spring-Verlag, 2^nd Printing 1994, p80;

[9] Orazio Svelto, "Principles of Lasers", 4^th edition, New York, Plenum Press, 1998, chapter 8;

[10] B. N. Chichkov et al., "Femtosecond, picosecond and nanosecond laser ablation of solids", Appl. Phys. A63, 109-115 (1996);

[11] Junlan Sun, Dazhi Jiang, "Vibrative cutting mechanism research and its applications", Mechanical Manufacturing (China), p6-7, 04/1997;

[12] Igor S. Grigoriev, Handbook of Physical Quantities, CRC press;

[13] R. Srinivasan, Bodil Braren, "Ultraviolet Laser Ablation of Organic Polymers", Chem. Rev. 1989, 89, 1303-1316;

[14] Wenwu Zhang, "Study on RPM, 3DM and Energy Field Formics," Proceedings of ICRPM'98, Beijing, p316-320;